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Journal articles on the topic 'Additive mapping'

Author: Grafiati

Published: 6 September 2023

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1

Cho, Young-Sun, and Hark-Mahn Kim. "Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings." Abstract and Applied Analysis 2007 (2007): 1–13. http://dx.doi.org/10.1155/2007/89180.

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We investigate the generalized Hyers-Ulam stability of the functional inequalities associated with Cauchy-Jensen additive mappings. As a result, we obtain that if a mapping satisfies the functional inequalities with perturbation which satisfies certain conditions, then there exists a Cauchy-Jensen additive mapping near the mapping.

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2

Bodaghi, Abasalt, Idham Arif Alias, Lida Mousavi, and Sedigheh Hosseini. "Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application." Journal of Function Spaces 2021 (November 11, 2021): 1–11. http://dx.doi.org/10.1155/2021/9943199.

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In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

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3

Rubin, Katy J., Gunnar Pruessner, and Grigorios A. Pavliotis. "Mapping multiplicative to additive noise." Journal of Physics A: Mathematical and Theoretical 47, no. 19 (April 23, 2014): 195001. http://dx.doi.org/10.1088/1751-8113/47/19/195001.

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4

Matos, Florinda, and Celeste Jacinto. "Additive manufacturing technology: mapping social impacts." Journal of Manufacturing Technology Management 30, no. 1 (January 21, 2019): 70–97. http://dx.doi.org/10.1108/jmtm-12-2017-0263.

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Purpose Recent developments in additive manufacturing (AM) technology have emphasized the issue of social impacts. However, such effects are still to be determined. So, the purpose of this paper is to map the social impacts of AM technology. Design/methodology/approach The methodological approach applied in this study combines a literature review with computer-aided content analysis to search for keywords related to social impacts. The content analysis technique was used to identify and count the relevant keywords in academic documents associated with AM social impacts. Findings The study found that AM technology social impacts are still in an exploratory phase. Evidence was found that several social challenges of AM technology will have an influence on the society. The topics associated with fabrication, customization, sustainability, business models and work emerged as the most relevant terms that can act as “pointers” to social impacts. Research limitations/implications The research on this subject is strongly conditioned by the scarcity of empirical experience and, consequently, by the scarcity of data and publications on the topic. Originality/value This study gives an up-to-date contribution to the topic of AM social impacts, which is still little explored in the literature. Moreover, the methodological approach used in this work combines bibliometrics with computer-aided content analysis, which also constitutes a contribution to support future literature reviews in any field. Overall, the results can be used to improve academic research in the topic and promote discussion among the different social actors.

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5

Bland, Stewart, and Brett Conner. "Mapping out the additive manufacturing landscape." Metal Powder Report 70, no. 3 (May 2015): 115–19. http://dx.doi.org/10.1016/j.mprp.2014.12.052.

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6

Dey, K. K., and A. C. Paul. "On the Trace of a Permuting Tri-additive Mapping in Left s_γ-unital Γ-rings." Journal of Scientific Research 3, no. 2 (April 28, 2011): 331–37. http://dx.doi.org/10.3329/jsr.v3i2.7278.

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Let M be 2 and 3 torsion-free left sΓ-unital Γ-rings. Let D: M ×M ×M ® M be a permuting tri-additive mapping with the trace d(x) = D(x,x,x). Let σ: M ® M be an endomorphism and τ: M ® M an epimorphism. The objective of this paper is to prove the following: a) If d is (σ,τ)-skew commuting on M, then D = 0; b) If d is (τ,τ)-skew-centralizing on M, then d is (τ,τ)-commuting on M; c) If d is 2-(σ,τ)-commuting on M, then d is (σ,τ)-commuting on M.Keywords: Permuting tri-additive mappings; Skew-commuting mappings; Skew-centralizing mappings; Commuting mappings.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.7278 J. Sci. Res. 3 (2), 331-337 (2011)

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7

Prieto Kullmer, Cesar N., Jacob A. Kautzky, Shane W. Krska, Timothy Nowak, Spencer D. Dreher, and David W. C. MacMillan. "Accelerating reaction generality and mechanistic insight through additive mapping." Science 376, no. 6592 (April 29, 2022): 532–39. http://dx.doi.org/10.1126/science.abn1885.

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Reaction generality is crucial in determining the overall impact and usefulness of synthetic methods. Typical generalization protocols require a priori mechanistic understanding and suffer when applied to complex, less understood systems. We developed an additive mapping approach that rapidly expands the utility of synthetic methods while generating concurrent mechanistic insight. Validation of this approach on the metallaphotoredox decarboxylative arylation resulted in the discovery of a phthalimide ligand additive that overcomes many lingering limitations of this reaction and has important mechanistic implications for nickel-catalyzed cross-couplings.

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8

Galletti, Ardelio, and Antonio Maratea. "Mapping the reliability of the additive log-ratio transformation." International Journal of Internet Technology and Secured Transactions 7, no. 1 (2017): 71. http://dx.doi.org/10.1504/ijitst.2017.085736.

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9

Maratea, Antonio, and Ardelio Galletti. "Mapping the reliability of the additive log-ratio transformation." International Journal of Internet Technology and Secured Transactions 7, no. 1 (2017): 71. http://dx.doi.org/10.1504/ijitst.2017.10006659.

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10

French, J. L. "Generalized additive models for cancer mapping with incomplete covariates." Biostatistics 5, no. 2 (April 1, 2004): 177–91. http://dx.doi.org/10.1093/biostatistics/5.2.177.

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11

Wood, Jay A. "Isometry groups of additive codes over finite fields." Journal of Algebra and Its Applications 17, no. 10 (October 2018): 1850198. http://dx.doi.org/10.1142/s0219498818501980.

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When [Formula: see text] is a linear code over a finite field [Formula: see text], every linear Hamming isometry of [Formula: see text] to itself is the restriction of a linear Hamming isometry of [Formula: see text] to itself, i.e. a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping [Formula: see text] to itself is an additive Hamming isometry, but there may exist additive Hamming isometries that are not monomial transformations.The monomial transformations mapping [Formula: see text] to itself form a group [Formula: see text], and the additive Hamming isometries form a larger group [Formula: see text]: [Formula: see text]. The main result says that these two subgroups can be as different as possible: for any two subgroups [Formula: see text], subject to some natural necessary conditions, there exists an additive code [Formula: see text] such that [Formula: see text] and [Formula: see text].

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12

Ali, Asma, and Ambreen Bano. "Multiplicative (Generalized) Reverse Derivations on Semiprime Ring." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 717–29. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3248.

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Let R be a semiprime ring. A mapping F : R → R (not necessarily additive) is called a multiplicative (generalized) reverse derivation if there exists a map d : R → R (not necessarily a derivation nor an additive map) such that F(xy) = F(y)x + yd(x) for all x, y є R. In this paper we investigate some identities involving multiplicative (generalized) reverse derivation and prove some theorems in which we characterize these mappings.

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13

Fei, Xiuhai, and Haifang Zhang. "Nonlinear Jordan Derivable Mappings of Generalized Matrix Algebras by Lie Product Square-Zero Elements." Journal of Mathematics 2021 (September 9, 2021): 1–13. http://dx.doi.org/10.1155/2021/2065425.

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The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping Δ of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation δ and an additive antiderivation f . Moreover, δ and f are uniquely determined.

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14

Eskandani, G. Zamani, Ali Reza Zamani, and H. Vaezi. "Fuzzy approximation of an additive functional equation." Journal of Function Spaces and Applications 9, no. 2 (2011): 205–15. http://dx.doi.org/10.1155/2011/941731.

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In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation∑i=1mf(mxi+∑j=1, j≠imxj)+f(∑i=1mxi)=2f(∑i=1mmxi)in fuzzy Banach spaces and some applications of our results in the stability of above mapping from a normed space to a Banach space will be exhibited.

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15

Eidinejad, Zahra, Reza Saadati, and Hari M. Srivastava. "The Cauchy–Optimal Stability Results for Cauchy–Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space." Axioms 12, no. 4 (April 21, 2023): 405. http://dx.doi.org/10.3390/axioms12040405.

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In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy–Optimal stability (C–O-stability) for all defined mappings.

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16

Xu, Tian Zhou, and John Michael Rassias. "On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation inn-Banach Spaces." Abstract and Applied Analysis 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/926390.

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The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation inn-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.

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17

Baron, Karol. "On Orthogonally Additive Functions With Big Graphs." Annales Mathematicae Silesianae 31, no. 1 (September 26, 2017): 57–62. http://dx.doi.org/10.1515/amsil-2016-0016.

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Abstract Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

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18

Brešar, Matej. "On skew-commuting mappings of rings." Bulletin of the Australian Mathematical Society 47, no. 2 (April 1993): 291–96. http://dx.doi.org/10.1017/s0004972700012521.

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A mapping f of a ring R into itself is called skew-commuting on a subset S of R if f(s)s + sf(s) = 0 for all s ∈ S. We prove two theorems which show that under rather mild assumptions a nonzero additive mapping cannot have this property. The first theorem asserts that if R is a prime ring of characteristic not 2, and f: R → R is an additive mapping which is skew-commuting on an ideal I of R, then f(I) = 0. The second theorem states that zero is the only additive mapping which is skew-commuting on a 2-torsion free semiprime ring.

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19

Azadi Kenary, Hassan, Themistocles M. Rassias, H. Rezaei, S. Talebzadeh, and Won-Gil Park. "Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping." Discrete Dynamics in Nature and Society 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/824257.

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20

Murali, R., and A. Antony Raj. "Isometries of Euler - Lagrange Additive Mapping in Quasi- Banach Spaces." International Journal of Mathematics Trends and Technology 25, no. 1 (September 25, 2015): 27–31. http://dx.doi.org/10.14445/22315373/ijmtt-v25p505.

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21

FOŠNER, MAJA, NADEEM UR REHMAN, and JOSO VUKMAN. "An Engel condition with an additive mapping in semiprime rings." Proceedings - Mathematical Sciences 124, no. 4 (November 2014): 497–500. http://dx.doi.org/10.1007/s12044-014-0205-4.

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22

Zaitov, A. A. "Open mapping theorem for spaces of weakly additive homogeneous functionals." Mathematical Notes 88, no. 5-6 (December 2010): 655–60. http://dx.doi.org/10.1134/s0001434610110052.

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23

Farah, Ilijas. "Completely Additive Liftings." Bulletin of Symbolic Logic 4, no. 1 (March 1998): 37–54. http://dx.doi.org/10.2307/421005.

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The purpose of this communication is to survey a theory of liftings, as developed in author's thesis ([8]). The first result in this area was Shelah's construction of a model of set theory in which every automorphism of P(ℕ)/ Fin, where Fin is the ideal of finite sets, is trivial, or inother words, it is induced by a function mapping integers into integers ([33]). (It is a classical result of W. Rudin [31] that under the Continuum Hypothesis there are automorphisms other than trivial ones.) Soon afterwards, Velickovic ([47]), was able to extract from Shelah's argument the fact that every automorphism of P(ℕ)/ Fin with a Baire-measurable lifting has to be trivial. This, for instance, implies that in Solovay's model ([36]) all automorphisms are trivial. Later on, an axiomatic approach was adopted and Shelah's conclusion was drawn first from the Proper Forcing Axiom (PFA) ([34]) and then from the milder Open Coloring Axiom (OCA) and Martin's Axiom (MA) ([48], see §5 for definitions). Both shifts from the quotient P(ℕ)/ Fin to quotients over more general ideals P(ℕ)/I and from automorphisms to arbitrary ho-momorphisms were made by Just in a series of papers ([14]-[17]), motivated by some problems in algebra ([7, pp. 38–39], [43, I.12.11], [45, Q48]) and topology ([46, p. 537]).

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24

Gordji, M. Eshaghi, M. B. Ghaemi, G. H. Kim, and Badrkhan Alizadeh. "Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation." Journal of Applied Mathematics 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/726020.

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Let be an algebra, and let , be ring automorphisms of . An additive mapping is called a -derivation if for all . Moreover, an additive mapping is said to be a generalized -derivation if there exists a -derivation such that for all . In this paper, we investigate the superstability of generalized -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

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25

Klahn, Christoph, Filippo Fontana, Bastian Leutenecker-Twelsiek, and Mirko Meboldt. "Mapping value clusters of additive manufacturing on design strategies to support part identification and selection." Rapid Prototyping Journal 26, no. 10 (October 26, 2020): 1797–807. http://dx.doi.org/10.1108/rpj-10-2019-0272.

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Purpose Additive manufacturing (AM) allows companies to create additional value in the processes of new product development and order fulfillment. One of the challenges for engineers is to identify suitable parts and applications for additive manufacturing. The purpose of this paper is to investigate the relation between value creation and the design process. The implications of this relation provide an orientation on the methods for identifying parts and applications for additive manufacturing. Design/methodology/approach Mapping the value clusters of AM on design strategies allows determining the expected degree of change in design. A classification into major and minor design changes is introduced to describe the predictability of the impact of AM on past performance and business model. The ability to predict the future properties of an AM part determines the suitability of identification and selection methods from literature. The mapping is validated by an identification process that creates a shortlist of potential AM parts based on the strategic decision for a value cluster. Shortlisted parts are then evaluated based on the criteria technology readiness, required post-processing, customer benefit and manufacturer benefit. Findings The mapping of value clusters on expected design changes determines the type of selection process. For minor design changes, automated part identification serves as a powerful tool while major design changes require the judgment of skilled engineers. Research limitations/implications The mapping of value clusters to design strategies and degree of change in design is based on empirical observations and conclusions. The mapping has been validated in an industrial context in different identification and selection processes. Nevertheless the versatility of AM and industrial environments impede a universal validity of high-level concepts. Practical implications This value-driven process of identification and selection was applied in technology transfer projects and proved to be useful for AM novices and experts. The mapping supports the identification and selection process, as well as the general product development process by providing an indication of the design effort for implementing AM. Originality/value The novel mapping links the economic domain of value creation to the engineering domain of design strategies to provide guidance in the selection of economically and technically suitable parts for additive manufacturing.

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26

Al Subaiei, Bana, and Noômen Jarboui. "A Rickart-Like Theorem for the Additivity of Multiplicative Maps on Rings." Journal of Mathematics 2022 (April 13, 2022): 1–4. http://dx.doi.org/10.1155/2022/5052308.

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Rickart’s theorem states that every bijective multiplicative mapping of a Boolean ring R onto an arbitrary ring S is necessarily additive. We prove a version of Rickart’s theorem for non-bijective mappings. This enables us to partially answer a question that was left open (Al Subaiei, B., Jarboui, N. On the Monoid of Unital Endomorphisms of a Boolean Ring. Axioms 2021, 10, 305).

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27

Brzdęk, Janusz. "On Ulam's Type Stability of the Cauchy Additive Equation." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/540164.

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We prove a general result on Ulam's type stability of the functional equationfx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.

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28

Patterson, Albert E., Charul Chadha, and Iwona M. Jasiuk. "Identification and Mapping of Manufacturability Constraints for Extrusion-Based Additive Manufacturing." Journal of Manufacturing and Materials Processing 5, no. 2 (April 10, 2021): 33. http://dx.doi.org/10.3390/jmmp5020033.

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This article develops and demonstrates a set of design-focused manufacturability constraints for the fused deposition modeling/fused filament fabrication (FDM/FFF) process. These can be mapped from the basic behavior and process characteristics and formulated in terms of implicit or explicit design constraints. When the FDM/FFF process is explored and examined for its natural limitations and behavior, it can provide a set of manufacturing considerations (advantages, limitations, and best practices). These can be converted into manufacturing constraints, which are practical limits on the ability of the process. Finally, these can be formulated in terms of design–useful manufacturability constraints. Many of the constants and parameters must be determined experimentally for specific materials. The final list of 54 major manufacturability constraints presented in this work will better inform designers considering using FDM/FFF as a manufacturing process, and help guide design decisions. After derivation and presentation of the constraint set, extensive discussion about practical implementation is provided at the end of the paper, including advice about experimentally determining constants and appropriate printing parameters. Finally, three case studies are presented which implement the constraints for simple design problems.

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29

Ashraf. "An Additive Mapping Satisfying an Algebraic Condition in Rings with Identity." Journal of Advanced Research in Pure Mathematics 5, no. 2 (April 1, 2013): 38–45. http://dx.doi.org/10.5373/jarpm.1333.022712.

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30

Zou, Bin, Jingwen Chen, Liang Zhai, Xin Fang, and Zhong Zheng. "Satellite Based Mapping of Ground PM2.5 Concentration Using Generalized Additive Modeling." Remote Sensing 9, no. 1 (December 22, 2016): 1. http://dx.doi.org/10.3390/rs9010001.

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31

Park, Choonkil, and Jae Myoung Park. "Generalized Hyers–Ulam stability of an Euler–Lagrange type additive mapping." Journal of Difference Equations and Applications 12, no. 12 (December 2006): 1277–88. http://dx.doi.org/10.1080/10236190600986925.

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32

Najati, Abbas, and Choonkil Park. "The Pexiderized Apollonius–Jensen type additive mapping and isomorphisms betweenC*-algebras." Journal of Difference Equations and Applications 14, no. 5 (May 2008): 459–79. http://dx.doi.org/10.1080/10236190701466546.

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33

Baak, Choonkil, Deok-Hoon Boo, and Themistocles M. Rassias. "Generalized additive mapping in Banach modules and isomorphisms between C∗-algebras." Journal of Mathematical Analysis and Applications 314, no. 1 (February 2006): 150–61. http://dx.doi.org/10.1016/j.jmaa.2005.03.099.

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34

Wang, Rui Dong, and Xu Jian Huang. "Isometries and additive mapping on the unit spheres of normed spaces." Acta Mathematica Sinica, English Series 33, no. 10 (July 20, 2017): 1431–42. http://dx.doi.org/10.1007/s10114-017-6589-1.

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35

Yass, Shaima'a. "On Additive Mapping with Period 3 on Rings and Near-Rings." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 1 (October 7, 2021): 259–73. http://dx.doi.org/10.55562/jrucs.v42i1.168.

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In this research we introduced the definition of a map with period 3 on a ring Ɍ and on right ( left ) ideal Ῑ of Ɍ, then we prove that, when Ɍ is a prime ring with char (Ɍ)  2, and Ῑ  0, Ῑ is right ideal on Ɍ, if đ is a derivation with period 3 in Ɍ,then either đ=0, or u2=0 uῙ. Also we proved, when Ɍ is a domain with 1, and char (Ɍ)  6, If δ is a right generalized derivation on Ɍ with period 3, then δ is the identity map. Lastly, we define a map with Period 3 on near-rings, and gived results for prime left near-rings with maps acts as an anti-homomorphism (or homomorphism), with period 3, to obtain commuatative rings.

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36

Ashraf, M., and A. Jabeen. "Characterizations of additive -Lie derivations on unital algebras." Ukrains’kyi Matematychnyi Zhurnal 73, no. 4 (April 21, 2021): 455–66. http://dx.doi.org/10.37863/umzh.v73i4.838.

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UDC 512.5 Let be a commutative ring with unity and be a unital algebra over (or field ).An -linear map is called a Lie derivation on if holds for all For scalar an additive map is called an additive -Lie derivation on if where holds for all In the present paper, under certain assumptions on it is shown that every Lie derivation (resp., additive -Lie derivation) on is of standard form, i.e., where is an additive derivation on and is a mapping vanishing at with in Moreover, we also characterize the additive -Lie derivation for by its action at zero product in a unital algebra over

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37

Lee, Yang-Hi, and Gwang Kim. "Generalized Hyers–Ulam Stability of the Additive Functional Equation." Axioms 8, no. 2 (June 25, 2019): 76. http://dx.doi.org/10.3390/axioms8020076.

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We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

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38

Balcerzak, M., S. A. Belov, and V. V. Chistyakov. "On Helly's principle for metric semigroup valued BV mappings to two real variables." Bulletin of the Australian Mathematical Society 66, no. 2 (October 2002): 245–57. http://dx.doi.org/10.1017/s0004972700040090.

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We introduce a concept of metric space valued mappings of two variables with finite total variation and define a counterpart of the Hardy space. Then we establish the following Helly type selection principle for mappings of two variables: Let X be a metric space and a commutative additive semigroup whose metric is translation invariant. Then an infinite pointwise precompact family of X-valued mappings on the closed rectangle of the plane, which is of uniformly bounded total variation, contains a pointwise convergent sequence whose limit is a mapping with finite total variation.

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39

Krasikova, I., O. Fotiy, M. Pliev, and M. Popov. "ON SEPARATE ORDER CONTINUITY OF ORTHOGONALLY ADDITIVE OPERATORS." Bukovinian Mathematical Journal 9, no. 1 (2021): 200–209. http://dx.doi.org/10.31861/bmj2021.01.17.

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Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping f : E → F between vector lattices E and F is horizontally-to-order continuous provided f sends laterally increasing order convergent nets in E to order convergent nets in F, and f is uniformly-to-order continuous provided f sends uniformly convergent nets to order convergent nets).

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40

Zamani, Zahra, Bahman Yousefi, and Hassan Azadi Kenary. "Fuzzy Hyers-Ulam-Rassias stability for generalized additive functional equations." Boletim da Sociedade Paranaense de Matemática 40 (January 30, 2022): 1–14. http://dx.doi.org/10.5269/bspm.43662.

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In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

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41

Petrov, Evgeniy, and Ruslan Salimov. "Quasisymmetric mappings in b-metric spaces." Ukrainian Mathematical Bulletin 18, no. 1 (March 9, 2021): 60–70. http://dx.doi.org/10.37069/1810-3200-2021-18-1-4.

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Considering quasisymmetric mappings between b-metric spaces we have found a new estimation for the ratio of diameters of two subsets which are images of two bounded subsets. This result generalizes the well-known Tukia-Vaisala inequality. The condition under which the image of a b-metric space under a quasisymmetric mapping is also a b-metric space is established. Moreover, the latter question is investigated for additive metric spaces.

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42

Toumi, Mohamed Ali. "CONTINUOUS GENERALIZED (θ, ϕ)-SEPARATING DERIVATIONS ON ARCHIMEDEAN ALMOST f-ALGEBRAS." Asian-European Journal of Mathematics 05, no. 03 (September 2012): 1250045. http://dx.doi.org/10.1142/s1793557112500453.

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Let A be an ℓ-algebra and let θ and ϕ be two endomorphisms of A. The couple (θ, ϕ) is called to be separating if xy = 0 implies θ(x)ϕ(y) = 0. If in addition θ and ϕ are ring endomorphisms of A, then the couple (θ, ϕ) is said to be ring-separating. An additive mapping δ : A → A is called (θ, ϕ)-separating derivation on A if there exists a (θ, ϕ)-separating couple with δ(xy) = δ(x)θ(y) + ϕ(x)δ(y), holds for all x, y ∈ A. If an addition θ, ϕ and δ are continuous, then δ is called a continuous (θ, ϕ)-ring-separating derivation. If in addition the couple (θ, ϕ) is ring-separating then δ is called a continuous (θ, ϕ)-ring-separating derivation. An additive mapping F : A → A is called a continuous generalized (θ, ϕ)-separating derivation on A if F is continuous mapping and if there exists a derivation d : A → A such that θ and ϕ are continuous, (θ, ϕ) is a separating couple and F(xy) = F(x)θ(y) + ϕ(x)d(y), holds for all x, y ∈ A. In this paper, we give a description of continuous (θ, ϕ)-ring-separating derivations on some ℓ-algebras. This generalizes a well-known theorem by Colville, Davis, and Keimel [Positive derivations on f-rings, J. Austral. Math. Soc23 (1977) 371–375] and generalizes the results of Boulabiar in [Positive derivations on almost f-rings, Order19 (2002) 385–395], Ben Amor [On orthosymmetric bilinear maps, Positivity14(1) (2010) 123–130] and Toumi et al. in [Order bounded derivations on Archimedean almost f-algebras, Positivity14(2) (2010) 239–245]. Moreover, inspiring from [Toumi, Order-bounded generalized derivations on Archimedean almost f-algebras, Commun. Algebra38(1) (2010) 154–164], it is shown that the notion of continuous generalized (θ, ϕ)-separating derivation on an archimedean almost f-algebra A is the concept of generalized θ-multiplier, that is an additive mapping satisfying F(xyz) = F(x)θ(yz), for all x, y, z ∈ A. In the case where A is an archimedean f-algebra, the situation improves. Indeed, the collection of all continuous generalized (θ, ϕ)-separating derivation on A coincides with the concept of θ-multiplier, that is an additive mapping satisfying F(xy) = F(x)θ(y), for all x, y ∈ A. If in addition A is a Dedekind complete vector lattice and θ is a positive mapping, then the set of all order bounded generalized of the form (θ, ϕ)-separating derivations on A, under composition, is an archimedean lattice-ordered algebra.

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Alwan, Haneen, and Zahir Hussain. "A Multiplicative-Additive Chaotic-Address Steganography." Journal of Kufa for Mathematics and Computer 7, no. 2 (November 1, 2021): 16–25. http://dx.doi.org/10.31642/jokmc/2018/070204.

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In this study, Multiple-Chaotic maps were merged by using multiplicative-additive form to generate the chaotic sequences which are used to track the addresses of shuffled bits in steganography. Three techniques are introduced for image steganography in the spatial domain. The first system is based on the well-known LSB technique, the second system is based on looking for the identical bits between the secret message and the cover image and the third system is based on the concept of LSB substitution, it is employed the mapping of secret data bits with cover pixel bits. It was tested and evaluated security levels for the proposed techniques by using the Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), histogram analysis and correlative analysis and tested the Chaotic sequences generated by using correlation, Lypaunov exponents, Poincaré section and 0-1Test. The results show that the proposed methods perform better than existed systems.

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44

Gordji, M. Eshaghi, M. B. Ghaemi, and H. Majani. "Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces." Discrete Dynamics in Nature and Society 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/162371.

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We introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces.

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Oda, Hiroyoshi, Makoto Tsukada, Takeshi Miura, Yuji Kobayashi, and Sin-Ei Takahasi. "The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples." International Journal of Mathematics and Mathematical Sciences 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/109754.

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We give an Ulam type stability result for the following functional equation:f(αx−αx′+x0)=βf(x)−βf(x′)+y0 (for all x,x′∈X)under a suitable condition. We also give a concrete stability result for the case taking upδ∥x∥p∥x′∥qas a control function.

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Kellens, Karel, Martin Baumers, Timothy G. Gutowski, William Flanagan, Reid Lifset, and Joost R. Duflou. "Environmental Dimensions of Additive Manufacturing: Mapping Application Domains and Their Environmental Implications." Journal of Industrial Ecology 21, S1 (August 1, 2017): S49—S68. http://dx.doi.org/10.1111/jiec.12629.

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Park, Choonkil, Hassan Azadi Kenary, and Najmeh Sahami. "Non-Archimedean and random HUR-approximation of a Cauchy-Jensen additive mapping." Journal of Inequalities and Applications 2014, no. 1 (2014): 209. http://dx.doi.org/10.1186/1029-242x-2014-209.

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Zancul, Eduardo De Senzi, Luiz Fernando C. S. Durao, Alexandre M. Rocha, and Gabriel Delage e. Silva. "PLM process and information mapping for mass customisation based on additive manufacturing." International Journal of Product Lifecycle Management 9, no. 2 (2016): 159. http://dx.doi.org/10.1504/ijplm.2016.079770.

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E Silva, Gabriel Delage, Alexandre M. Rocha, Luiz Fernando C. S. Durao, and Eduardo De Senzi Zancul. "PLM process and information mapping for mass customisation based on additive manufacturing." International Journal of Product Lifecycle Management 9, no. 2 (2016): 159. http://dx.doi.org/10.1504/ijplm.2016.10000602.

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Zhao, Hao, Alistair Ho, Alec Davis, Alphons Antonysamy, and Philip Prangnell. "Automated image mapping and quantification of microstructure heterogeneity in additive manufactured Ti6Al4V." Materials Characterization 147 (January 2019): 131–45. http://dx.doi.org/10.1016/j.matchar.2018.10.027.

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