Relevant bibliographies by topics / Generalized Metric Spaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Generalized Metric Spaces'

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Published: 5 October 2024

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Journal articles on the topic "Generalized Metric Spaces"

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BEG, ISMAT, MUJAHID ABBAS, and TALAT NAZIR. "GENERALIZED CONE METRIC SPACES." Journal of Nonlinear Sciences and Applications 03, no. 01 (February 13, 2010): 21–31. http://dx.doi.org/10.22436/jnsa.003.01.03.

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Ali, Basit, Hammad Ali, Talat Nazir, and Zakaria Ali. "Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces." Mathematics 11, no. 21 (October 26, 2023): 4445. http://dx.doi.org/10.3390/math11214445.

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In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.
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D, Ramesh Kumar. "Generalized Rational Inequalities in Complex Valued Metric Spaces." Journal of Computational Mathematica 1, no. 2 (December 30, 2017): 121–32. http://dx.doi.org/10.26524/cm21.

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Adewale, O. K., J. O. Olaleru, H. Olaoluwa, and H. Akewe. "Fixed Point Theorems on Generalized Rectangular Metric Spaces." Journal of Mathematical Sciences: Advances and Applications 65, no. 1 (April 10, 2021): 59–84. http://dx.doi.org/10.18642/jmsaa_7100122185.

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In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.
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La Rosa, Vincenzo, and Pasquale Vetro. "Common fixed points for α-ψ-φ-contractions in generalized metric spaces." Nonlinear Analysis: Modelling and Control 19, no. 1 (January 20, 2014): 43–54. http://dx.doi.org/10.15388/na.2014.1.3.

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We establish some common fixed point theorems for mappings satisfying an α-ψ-ϕcontractive condition in generalized metric spaces. Presented theorems extend and generalize manyexisting results in the literature. Erratum to “Common fixed points for α-ψ-φ-contractions in generalized metric spaces” In Example 1 of our paper [V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕcontractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19(1):43–54, 2014] a generalized metric has been assumed. Nevertheless some mistakes have appeared in the statement. The aim of this note is to correct this situation.
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Yang, Hui. "Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces." Mathematics 11, no. 24 (December 14, 2023): 4962. http://dx.doi.org/10.3390/math11244962.

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In this paper, we first propose the concept of a family of quasi-G-metric spaces corresponding to the tripled fuzzy metric spaces (or G-fuzzy metric spaces). Using their properties, we give the characterization of tripled fuzzy metrics. Second, we introduce the notion of generalized fuzzy Meir–Keeler-type contractions in G-fuzzy metric spaces. With the aid of the proposed notion, we show that every orbitally continuous generalized fuzzy Meir–Keeler-type contraction has a unique fixed point in complete G-fuzzy metric spaces. In the end, an example illustrates the validity of our results.
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Karapınar, Erdal. "Discussion onα-ψContractions on Generalized Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/962784.

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We discuss the existence and uniqueness of fixed points ofα-ψcontractive mappings in complete generalized metric spaces, introduced by Branciari. Our results generalize and improve several results in the literature.
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Zhang, Wei, and Chenxi Ouyang. "GENERALIZED CONE METRIC SPACES AND ORDERED SPACES." Far East Journal of Applied Mathematics 101, no. 2 (March 15, 2019): 101–12. http://dx.doi.org/10.17654/am101020101.

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Brock, Paul. "Probabilistic convergence spaces and generalized metric spaces." International Journal of Mathematics and Mathematical Sciences 21, no. 3 (1998): 439–52. http://dx.doi.org/10.1155/s0161171298000611.

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The categoryPPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom(Δ)and whose morphisms are continuous mappings, is introduced. Categories consisting of generalized metric spaces as objects and contraction mappings as morphisms are embedded as full subcategories ofPPRS(Δ). The embeddings yield a description of metric spces and their most natural generalizations entirely in terms of convergence criteria.
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Liftaj, Silvana, Eriola Sila, and Zamir Selko. "Generalized almost Contractions on Extended Quasi-Cone B-Metric Spaces." WSEAS TRANSACTIONS ON MATHEMATICS 22 (November 29, 2023): 894–903. http://dx.doi.org/10.37394/23206.2023.22.98.

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Fixed Point Theory is among the most valued research topics nowadays. Over the years, it has been developed in three directions: by generalizing the metric space, by establishing new contractive conditions, and by applying its results to various fields such as Differential Equations, Integral Equations, Economics, etc. In this paper, we define a new class of cone metric spaces called the class of extended quasi-cone b-metric spaces. Extended quasi-cone b-metric spaces generalize cone metric spaces and quasi-cone b-metric spaces. We have studied topological issues, such as the right and left topologies, right (left) Cauchy, and convergent sequences. Furthermore, there are determined generalized τ-almost contractions, which extend the almost contractions. The highlight of this study is the investigation of the existence and uniqueness of a fixed point for some types of generalized τ-almost contractions in extended quasi-cone b-metric space. We prove some corollaries and theorems for known contractions in extended quasi-cone b-metric spaces. Our results generalize some known theorems given in literature due to the new cone metric spaces and contractions. Concrete examples illustrate theoretical outcomes. In addition, we show an application of the main results to Integral Equations, which provides the applicative side of them.
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Dissertations / Theses on the topic "Generalized Metric Spaces"

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Sarkis, Ralph. "Lifting Algebraic Reasoning to Generalized Metric Spaces." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0025.

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On retrouve le raisonnement algébrique partout en mathématique et en informatique, et il a déjà été généralisé à pleins de contextes différents. En 2016, Mardare, Panangaden et Plotkin ont introduit les algèbres quantitatives, c'est-à-dire, des espaces métriques équipés d'opérations 1-lipschitzienne relativement à la métrique. Ils ont prouvées des homologues à des résultats importants en algèbre universelle, et en particulier ils ont donné un système de déduction correct et complet qui généralise la logique équationnelle de Birkhoff en remplaçant l'égalité par l'égalité à \varepsilon près. Ça leur a permis de donner une axiomatisation algébrique pour quelques métriques importantes comme la distance de Hausdorff et celle de Kantorovich.Dans cette thèse, on modifie deux aspects du cadre de Mardare et al. Premièrement, on remplace les métriques par une notion plus générale qui englobe les pseudométriques, les ordres partiels, les métriques probabilistes, entre autres. Deuxièmement, on n'exige pas que les operations de nos algèbres quantitatives soient lipschitzienne. On donne un système de déduction correct et complet, on construit les algèbres quantitatives libres, et on démontre la valeur de notre généralisation en prouvant que toute monade sur les espaces métriques généralisés qui est le relèvement d'une monade finitaire sur les ensembles peut être présentée par une théorie algébrique quantitative. On applique ce dernier résultat pour obtenir une axiomatisation de la distance de \L ukaszyk--Karmowski
Algebraic reasoning is ubiquitous in mathematics and computer science, and it has been generalized to many different settings. In 2016, Mardare, Panangaden, and Plotkin introduced quantitative algebras, that is, metric spaces equipped with operations that are nonexpansive relative to the metric. They proved counterparts to important results in universal algebra, and in particular they provided a sound and complete deduction system generalizing Birkhoff's equational logic by replacing equality with equality up to \varepsilon. This allowed them to give algebraic axiomatizations for several important metrics like the Hausdorff and Kantorovich distances.In this thesis, we make two modifications to Mardare et al.'s framework. First, we replace metrics with a more general notion that captures pseudometrics, partial orders, probabilistic metrics, and more. Second, we do not require the operations in a quantitative algebra to be nonexpansive. We provide a sound and complete deduction system, we construct free quantitative algebras, and we demonstrate the value of our generalization by proving that any monad on generalized metric spaces that lifts a monad on sets can be presented with a quantitative algebraic theory. We apply this last result to obtain an axiomatization for the \L ukaszyk--Karmowski distance
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Miravet, Fortuño David. "GENERALIZED FUZZY METRIC SPACES DEFINED BY MEANS OF T-NORMS." Doctoral thesis, Universitat Politècnica de València, 2019. http://hdl.handle.net/10251/124816.

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[ES] En 1965 L. Zadeh introdujo el concepto de conjunto fuzzy, estableciendo una nueva línea de investigación, conocida como matemática fuzzy. Desde entonces, varios autores han estado investigando la construcción de una definición consistente de espacio métrico fuzzy. En 1994, George y Veeramani introdujeron y estudiaron un concepto de espacio métrico fuzzy, que era una adecuada modificación del concepto dado por Kramosil y Michalek. Estos conceptos han sido estudiados y desarrollados en diversas líneas durante los últimos 25 años. Con la intención de contribuir a este desarrollo de la teoría fuzzy, en esta tesis hemos introducido y estudiado los siguientes ítems: 1. Hemos introducido el concepto de espacio métrico fuzzy extendido M0, que es una extensión adecuada de una GV-métrica fuzzy donde el parámetro t puede tomar el valor 0. Además, hemos estudiado conceptos relacionados con la convergencia y las sucesiones de Cauchy en este contexto, así como teoremas sobre contractividad y punto fijo. 2. Hemos probado la existencia de sucesiones contractivas en el sentido de D.Mihet en un espacio métrico fuzzy en el sentido de George y Veeramani que no son de Cauchy. En consecuencia, hemos introducido y estudiado un concepto adecuado de sucesión estrictamente contractiva y hemos corregido el Lema 3.2 de [V. Gregori and J.J. Miñana, On fuzzy psi-contractive sequences and fixed point theorems, Fuzzy Sets and Systems 300 (2016), 93-101]. 3. Hemos introducido y estudiado una noción de (GV-)espacio métrico parcial fuzzy (X,P,*) sin ninguna condición adicional sobre la t-norma *. Después, hemos definido una topologia T_P sobre X deducida de P y hemos demostrado que (X,T_P) es un espacio T0. 4. Hemos relacionado el mencionado concepto de GV-espacio métrico parcial fuzzy con la noción de GV-espacio casi-métrico fuzzy definido por Gregori y Romaguera en [V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Applied General Topology 5 (2004), 129-136]. Se ha estudiado una dualidad entre estos espacios, imitando las técnicas utilizadas por Matthews en [S.G.Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183-197].
[CAT] En 1965, L. Zadeh va introduir el concepte de conjunt fuzzy, establint una nova línia d'investigació, coneguda com matemàtica fuzzy. Des d'aquell moment, molts autors han investigat la construcció d'una definició consistent d'espai mètric fuzzy. En 1994, George i Veeramani van introduir i estudiar una noció d'espai mètric fuzzy, realitzant una modificació adequada del concepte donat per Kramosil i Michalek. Aquests conceptes han estat estudiats i desenvolupats en diversos sentits durant els últims 25 anys. Amb la intenció de contribuir a aquest desenvolupament de la teoria fuzzy, en aquesta tesi hem introduït i estudiat els següents continguts: 1. Hem introduït el concepte d'espai mètric extés M0, que és una extensió adequada d'una GV -mètrica fuzzy M on el paràmetre t pot prendre el valor 0. A més, hem estudiat conceptes relacionats amb la convergència i les successions de Cauchy en aquest context, així com teoremes sobre contractivitat i punt fixe. 2. Hem provat l'existència de successions contractives en el sentit de D. Mihet en un GV -espai mètric fuzzy que no són Cauchy. Conseqüentment, hem aportat i estudiat un concepte apropiat de successió estrictament contractiva i hem corregit el Lema 3.2 de [V. Gregori and J.J. Miñana, On fuzzy psi-contractive sequences and fixed point theorems, Fuzzy Sets and Systems 300 (2016), 93-101]. 3. Hem introduït i estudiat una noció de (GV -)espai mètric parcial fuzzy (X,P,*) sense cap tipus de condició addicional sobre la t-norma contínua *. A continuació, hem definit una topologia T_P sobre X deduïda de P i hem demostrat que (X, T_P) es un espai T0. 4. Hem relacionat el ja mencionat concepte de GV -espai mètric parcial fuzzy amb la noció de GV -espai quasi-mètric fuzzy definit per Gregori i Romaguera en [V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Applied General Topology 5 (2004), 129-136]. S'ha estudiat una dualitat entre ambdós espais, imitant les tècniques utilitzades per Matthews en [S.G.Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183-197].
[EN] In 1965, L. Zadeh introduced the concept of fuzzy set, and thus established a new topic of research, known as fuzzy mathematics. Since then, several authors have been investigating the approach of a consistent fuzzy metric space theory. In 1994, George and Veeramani introduced and studied a concept of fuzzy metric space which was a proper modification of the concept given by Kramosil and Michalek. These notions have been studied and developed in several ways during the last 25 years. With the purpose of contributing to the development of the study of the fuzzy theory, in this thesis we have introduced and studied the following items: 1. We have introduced the concept of extended fuzzy metric M0 which is an appropriate extension of a GV -fuzzy metric M where the parameter t can take the value 0. Furthermore, we have studied convergence and Cauchyness concepts in this context, as well as contractivity and fixed point theorems. 2. We have proved the existence of contractive sequences in the sense of D. Mihet in a GV -fuzzy metric space which are not Cauchy. Then we have given and studied an appropriate concept of strictly contractive sequence and we have corrected Lemma 3.2 of [V. Gregori and J.J. Miñana, On fuzzy psi-contractive sequences and fixed point theorems, Fuzzy Sets and Systems 300 (2016), 93-101]. 3. We have introduced and studied a concept of (GV -)fuzzy partial metric space (X,P,*) without any extra conditions on the continuous t-norm *. Then we have defined a topology T_P on X deduced from P and we have proved that (X, T_P) is a T0 space. 4. We have related the aforementioned notion of GV -fuzzy partial metric space with the concept of GV -fuzzy quasi-metric space given by Gregori and Romaguera in [V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Applied General Topology 5 (2004), 129-136]. A duality is studied by mimicking the techniques used in [S.G.Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183-197] by Matthews.
Miravet Fortuño, D. (2019). GENERALIZED FUZZY METRIC SPACES DEFINED BY MEANS OF T-NORMS [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124816
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Tran, Anh Tuyet. "1p spaces." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2238.

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Stares, Ian S. "Extension of functions and generalised metric spaces." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386678.

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Babus, Octavian Vladut. "Generalised distributivity and the logic of metric spaces." Thesis, University of Leicester, 2016. http://hdl.handle.net/2381/37701.

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The aim of the thesis is to work towards a many-valued logic over a commutative unital quantale and, at the same time, towards a generalisation of coalgebraic logic enriched over a commutative unital quantale Ω. This is done by noticing that the contravariant powerset adjunction can be generalised to categories enriched over a commutative unital quantale. From here we define categorical algebras for the monad generated by this adjunction. We finish by showing that these categorical algebras are algebras over Set with operations and equations, and show that in some cases we can restrict the arity of those operations to be finite.
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Shi, Xiaohui. "Graev Metrics and Isometry Groups of Polish Ultrametric Spaces." Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc271898/.

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This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a correspondence between the isomorphism group of a generalized tree and the isometry group of a Heine-Borel Polish ultrametric space is established. The concept of a weak inverse limit is introduced to capture the characterization of isomorphism groups of generalized trees. In Chapter 4, partial results of isometry groups of uncountable compact ultrametric spaces are given. It turns out that every compact ultrametric space has a unique countable orbital decomposition. An orbital space consists of disjoint orbits. An orbit subspace of an orbital space is actually a compact homogeneous ultrametric subspace.
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Ivana, Štajner-Papuga. "Uopštena konvolucija." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2001. https://www.cris.uns.ac.rs/record.jsf?recordId=5987&source=NDLTD&language=en.

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U ovoj tezi je definisana uopštena konvolucija koja pripada domenu pseudo-analize i ima veliku primenu u mnogim matematičkim teorijama, npr. u proba-bilističkim metričkim prostorima, PDJ, teorijama odlučivanja, sistema, kontrole i fazi brojeva. Dokazane su bitne osobine ove operacije sa funkcijama. Dokazana je veza izmedju pseudo-konvolucija baziranih na poluprstenima različitih klasa Definisana je (5, C/)-konvolucija bazirana na uslovno distributivnom poluprstenu ([0,1], S, U)).Dat je još jedan vid uopštenja konvolucije baziran na uopštenim pseudo-operacijama.
In this thesis the generalized convolution have been defined. This operation with functions has applications in different mathematical theo­ ries, for example in Probabilistic Metric Spaces, PDE, System and Control Theory, Fuzzy numbers. Some basic properties of this operation has been proved, as well as connection between generalized convolutions based on dif­ferent classes of semirings. (5, U)-convolution has been defined, as well as convolution based on generalized pseudo-operations.
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Jelena, Stojanov. "Anisotropic frameworks for dynamical systems and image processing." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2015. https://www.cris.uns.ac.rs/record.jsf?recordId=93698&source=NDLTD&language=en.

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The research topic of this PhD thesis is a comparative analysis of classical specic geometric frameworks and of their anisotropic extensions; the construction of three different types of Finsler frameworks, which are suitable for the analysis of the cancer cells population dynamical system; the development of the anisotropic Beltrami framework theory with the derivation of the evolution ow equations corresponding to different classes of anisotropic metrics, and tentative applications in image processing.
Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih geometrijskih radnih okruženja i njihovih anizotropnih proširenja; konstrukcija  tri Finslerova radna okruženja različitog tipa koja su pogodna za analizu dinamičkog  sistema populacije kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene dobijenih teorijskih rezultata u digitalnoj obradi slika.
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Popa-Fischer, Anca. "Generalized Kähler metrics on complex spaces and a supplement to a Theorem of Fornæss and Narasimhan." [S.l. : s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=960695028.

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Abbas, Mujahid. "Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/48470.

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Mathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence and uniqueness of such mappings which can be viewed as a positive contribution towards an advancement of metric fixed point theory iii) Initiative of soft fixed point theory in framework of soft metric spaces and proving the results lying at the intersection of soft set theory and fixed point theory which would help in establishing a bridge between these two flourishing areas of research. iv) This study is also a starting point for the future research in the area of fuzzy soft fixed point theory.
Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48470
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Books on the topic "Generalized Metric Spaces"

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Lin, Shou, and Ziqiu Yun. Generalized Metric Spaces and Mappings. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-216-8.

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Karapinar, Erdal, and Ravi P. Agarwal. Fixed Point Theory in Generalized Metric Spaces. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14969-6.

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Abate, Marco. Finsler metrics-- a global approach: With applications to geometric function theory. Berlin: Springer-Verlag, 1994.

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Lin, Shou, and Ziqiu Yun. Generalized Metric Spaces and Mappings. Atlantis Press (Zeger Karssen), 2016.

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Karapinar, Erdal, and Ravi P. Agarwal. Fixed Point Theory in Generalized Metric Spaces. Springer International Publishing AG, 2022.

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Fixed Point Theory in Generalized Metric Spaces. Springer International Publishing AG, 2023.

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Fundamentals of Signal Processing in Generalized Metric Spaces. CRC Press LLC, 2022.

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Busemann, Herbert. Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8). Princeton University Press, 2016.

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Popoff, Andrey. Fundamentals of Signal Processing in Generalized Metric Spaces: Algorithms and Applications. Taylor & Francis Group, 2022.

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Popoff, Andrey. Fundamentals of Signal Processing in Generalized Metric Spaces: Algorithms and Applications. Taylor & Francis Group, 2022.

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Book chapters on the topic "Generalized Metric Spaces"

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Kirk, William, and Naseer Shahzad. "Generalized Metric Spaces." In Fixed Point Theory in Distance Spaces, 133–39. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10927-5_13.

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Lin, Shou, and Ziqiu Yun. "Generalized Metric Spaces." In Atlantis Studies in Mathematics, 147–258. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-216-8_3.

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Lin, Shou, and Ziqiu Yun. "The Origin of Generalized Metric Spaces." In Atlantis Studies in Mathematics, 1–51. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-216-8_1.

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Manav, N. "Fixed-Point Theorems in Generalized Modular Metric Spaces." In Metric Fixed Point Theory, 89–111. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4896-0_5.

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Laal Shateri, Tayebe, and Ozgur Ege. "Modular Spaces and Fixed Points of Generalized Contractions." In Metric Fixed Point Theory, 71–87. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4896-0_4.

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Paunović, Marija V., Samira Hadi Bonab, and Vahid Parvaneh. "Weak-Wardowski Contractions in Generalized Triple-Controlled Modular Metric Spaces and Generalized Triple-Controlled Fuzzy Metric Spaces." In Soft Computing, 45–66. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9781003312017-4.

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Moltó, Aníbal, José Orihuela, Stanimir Troyanski, and Manuel Valdivia. "Generalized Metric Spaces and Locally Uniformly Rotund Renormings." In A Nonlinear Transfer Technique for Renorming, 49–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85031-1_3.

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Aydi, Hassen, and Stefan Czerwik. "Fixed Point Theorems in Generalized b-Metric Spaces." In Springer Optimization and Its Applications, 1–9. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74325-7_1.

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Konwar, Nabanita. "Results on Generalized Tripled Fuzzy b-Metric Spaces." In Forum for Interdisciplinary Mathematics, 137–50. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0668-8_8.

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Popoff, Andrey. "Signal Filtering Algorithms in Spaces with L-group Properties." In Fundamentals of Signal Processing in Generalized Metric Spaces, 93–132. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003275855-3.

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Conference papers on the topic "Generalized Metric Spaces"

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Goleţ, Ioan, Ciprian Hedrea, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On Generalized Contractions in Probabilistic Metric Spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636943.

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Tang, Yongye, and Yongfu Su. "New Generalized Contractions in Complete Cone Metric Spaces." In 2011 International Symposium on Computer Science and Society (ISCCS). IEEE, 2011. http://dx.doi.org/10.1109/isccs.2011.83.

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Li, Xiaofan, Yachao Zhang, Shiran Bian, Yanyun Qu, Yuan Xie, Zhongchao Shi, and Jianping Fan. "VS-Boost: Boosting Visual-Semantic Association for Generalized Zero-Shot Learning." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/123.

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Unlike conventional zero-shot learning (CZSL) which only focuses on the recognition of unseen classes by using the classifier trained on seen classes and semantic embeddings, generalized zero-shot learning (GZSL) aims at recognizing both the seen and unseen classes, so it is more challenging due to the extreme training imbalance. Recently, some feature generation methods introduce metric learning to enhance the discriminability of visual features. Although these methods achieve good results, they focus only on metric learning in the visual feature space to enhance features and ignore the association between the feature space and the semantic space. Since the GZSL method uses semantics as prior knowledge to migrate visual knowledge to unseen classes, the consistency between visual space and semantic space is critical. To this end, we propose relational metric learning which can relate the metrics in the two spaces and make the distribution of the two spaces more consistent. Based on the generation method and relational metric learning, we proposed a novel GZSL method, termed VS-Boost, which can effectively boost the association between vision and semantics. The experimental results demonstrate that our method is effective and achieves significant gains on five benchmark datasets compared with the state-of-the-art methods.
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Łenski, Włodzimierz, and Bogdan Szal. "On the approximation of functions by matrix means in the generalized Hölder metric." In Function Spaces VIII. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc79-0-9.

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Pistone, Paolo. "On Generalized Metric Spaces for the Simply Typed Lambda-Calculus." In 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2021. http://dx.doi.org/10.1109/lics52264.2021.9470696.

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Dahiya, Anita, Asha Rani, and Manoj Kumar. "Fixed points for cyclic µ-expansions in generalized metric spaces." In RECENT ADVANCES IN FUNDAMENTAL AND APPLIED SCIENCES: RAFAS2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4990341.

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Fadail, Zaid Mohammed, and Abd Ghafur Bin Ahmad. "Fixed point results of T-Kannan contraction on generalized distance in cone metric spaces." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882558.

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Kosal, Isil Arda, and Mahpeyker Ozturk. "Best proximity points for elliptic generalized geraghty contraction mappings in elliptic valued metric spaces." In 7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5078470.

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Ramadana, Yusuf, and Hendra Gunawan. "Boundedness of sublinear operator generated by Calderón-Zygmund operator on generalized weighted Morrey spaces over quasi-metric measure spaces." In INTERNATIONAL CONFERENCE ON MATHEMATICAL ANALYSIS AND ITS APPLICATIONS 2022 (IConMAA 2022): Analysis, Uncertainty, and Optimization. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0191768.

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Tummala, Kusuma, A. Sree Rama Murthy, V. Ravindranath, P. Harikrishna, and N. V. V. S. Suryanarayana. "Common fixed points of generalized (α, η)-geraghty rational type contraction in b-metric spaces." In CONTEMPORARY INNOVATIONS IN ENGINEERING AND MANAGEMENT. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0158562.

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Reports on the topic "Generalized Metric Spaces"

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Lynch, James F. A Higgs Universe and the flow of time. Woods Hole Oceanographic Institution, April 2024. http://dx.doi.org/10.1575/1912/69338.

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Theoretically considering velocities greater than c implies considering an observer’s past and extends the overall analysis into the complex plane. By using a series of rotations by i in the complex plane, one can create a four-lobed structure of “instants of time,” which together with considering matter and antimatter in the lobes and the +/- sense of the rotation, leads to a Higgs field representation of space and time. A 10x10 metric is developed for this system as well as a generalized spacetime interval. It is also shown that the Friedmann Equations are consistent with our “Higgs Cosmology” if generalized to a set of coupled equations that connect the forward and backward going solutions. Simple solutions for the forward and backward going universes are presented, and are shown to be consistent with the backward solution providing both inflation and a “cosmological constant” type of dark energy, Dark matter is also discussed and is hypothesized to be due to the mass of the four “Higgs sectors” as seen through the lens of relativity by an observer in our universe. A PowerPoint presentation on this work is presented at the end of the report as a supplement.
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