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Journal articles on the topic 'Integral operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Tariq, Muhammad, Sotiris K. Ntouyas, Hijaz Ahmad, Asif Ali Shaikh, Bandar Almohsen, and Evren Hincal. "A comprehensive review of Grüss-type fractional integral inequality." AIMS Mathematics 9, no. 1 (2023): 2244–81. http://dx.doi.org/10.3934/math.2024112.

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<abstract><p>A survey of results on Grüss-type inequalities associated with a variety of fractional integral and differential operators is presented. The fractional differential operators includes, Riemann-Liouville fractional integral operators, Riemann-Liouville fractional integrals of a function with respect to another function, Katugampola fractional integral operators, Hadamard's fractional integral operators, $ k $-fractional integral operators, Raina's fractional integral operators, tempered fractional integral operators, conformable fractional integrals operators, proportional fractional integrals operators, generalized Riemann-Liouville fractional integral operators, Caputo-Fabrizio fractional integrals operators, Saigo fractional integral operators, quantum integral operators, and Hilfer fractional differential operators.</p></abstract>

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2

Girardi, Maria, and Lutz Weis. "Integral operators with operator-valued kernels." Journal of Mathematical Analysis and Applications 290, no. 1 (February 2004): 190–212. http://dx.doi.org/10.1016/j.jmaa.2003.09.044.

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3

Jefferies, Brian, and Susumu Okada. "Pettis integrals and singular integral operators." Illinois Journal of Mathematics 38, no. 2 (June 1994): 250–72. http://dx.doi.org/10.1215/ijm/1255986799.

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4

Shahmurov, Rishad. "On Integral Operators with Operator-Valued Kernels." Journal of Inequalities and Applications 2010, no. 1 (2010): 850125. http://dx.doi.org/10.1155/2010/850125.

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5

Garetto, Claudia, Günther Hörmann, and Michael Oberguggenberger. "Generalized oscillatory integrals and Fourier integral operators." Proceedings of the Edinburgh Mathematical Society 52, no. 2 (May 28, 2009): 351–86. http://dx.doi.org/10.1017/s0013091506000915.

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AbstractIn this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.

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6

Korotkov, V. B. "Properties of integrals and partially integral operators." Siberian Mathematical Journal 33, no. 1 (1992): 166–68. http://dx.doi.org/10.1007/bf00972952.

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7

Butt, S. I., B. Bayraktar, and M. Umar. "SEVERAL NEW INTEGRAL INEQUALITIES VIA 𝐾-RIEMANN–LIOUVILLE FRACTIONAL INTEGRALS OPERATORS." Issues of Analysis 28, no. 1 (February 2021): 3–22. http://dx.doi.org/10.15393/j3.art.2021.8770.

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8

Vinogradov, S. A. "Continuity of perturbations of integral operators, Cauchy-type integrals, maximal operators." Journal of Soviet Mathematics 34, no. 6 (September 1986): 2033–39. http://dx.doi.org/10.1007/bf01741577.

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9

Owa, Shigeyoshi. "Certain integral operators." Proceedings of the Japan Academy, Series A, Mathematical Sciences 67, no. 3 (1991): 88–93. http://dx.doi.org/10.3792/pjaa.67.88.

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10

Carbery, A. "SINGULAR INTEGRAL OPERATORS." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 373–75. http://dx.doi.org/10.1112/blms/20.4.373.

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11

Nguon, Donara. "Bessel integral operators." Integral Transforms and Special Functions 25, no. 8 (March 14, 2014): 647–62. http://dx.doi.org/10.1080/10652469.2014.894040.

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12

Korotkov, V. B. "Convolution Integral Operators." Siberian Mathematical Journal 59, no. 4 (July 2018): 677–80. http://dx.doi.org/10.1134/s0037446618040092.

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13

Ahmad, Faiz. "Starlike integral operators." Bulletin of the Australian Mathematical Society 32, no. 2 (October 1985): 217–24. http://dx.doi.org/10.1017/s0004972700009916.

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14

Korotkov, V. B. "Partially integral operators." Siberian Mathematical Journal 30, no. 5 (1990): 727–30. http://dx.doi.org/10.1007/bf00971264.

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15

Pavlov, E. A. "Integral convolution operators." Mathematical Notes of the Academy of Sciences of the USSR 38, no. 1 (July 1985): 554–56. http://dx.doi.org/10.1007/bf01137467.

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16

Inayat Noor, Khalida, and Muhammad Aslam Noor. "On Integral Operators." Journal of Mathematical Analysis and Applications 238, no. 2 (October 1999): 341–52. http://dx.doi.org/10.1006/jmaa.1999.6501.

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17

Yee, Tat-Leung, Ka-Luen Cheung, and Kwok-Pun Ho. "Integral operators on local Orlicz-Morrey spaces." Filomat 36, no. 4 (2022): 1231–43. http://dx.doi.org/10.2298/fil2204231y.

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We establish a general principle on the boundedness of operators on local Orlicz-Morrey spaces. As applications of this principle, we obtain the boundedness of the Calder?n-Zygmund operators, the nonlinear commutators of the Calder?n-Zygmund operators, the oscillatory singular integral operators, the singular integral operators with rough kernels and the Marcinkiewicz integrals on the local Orlicz-Morrey spaces.

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18

Bouzeffour, Fethi. "Fractional Integrals Associated with the One-Dimensional Dunkl Operator in Generalized Lizorkin Space." Symmetry 15, no. 9 (September 8, 2023): 1725. http://dx.doi.org/10.3390/sym15091725.

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This paper explores the realm of fractional integral calculus in connection with the one-dimensional Dunkl operator on the space of tempered functions and Lizorkin type space. The primary objective is to construct fractional integral operators within this framework. By establishing the analogous counterparts of well-known operators, including the Riesz fractional integral, Feller fractional integral, and Riemann–Liouville fractional integral operators, we demonstrate their applicability in this setting. Moreover, we show that familiar properties of fractional integrals can be derived from the obtained results, further reinforcing their significance. This investigation sheds light on the utilization of Dunkl operators in fractional calculus and provides valuable insights into the connections between different types of fractional integrals. The findings presented in this paper contribute to the broader field of fractional calculus and advance our understanding of the study of Dunkl operators in this context.

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19

Zhang, Zhiqiang, Ghulam Farid, Sajid Mehmood, Chahn-Yong Jung, and Tao Yan. "Generalized k-Fractional Chebyshev-Type Inequalities via Mittag-Leffler Functions." Axioms 11, no. 2 (February 21, 2022): 82. http://dx.doi.org/10.3390/axioms11020082.

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Mathematical inequalities have gained importance and popularity due to the application of integral operators of different types. The present paper aims to give Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels. Several new results can be deduced for different integral operators, along with Riemann–Liouville fractional integrals by substituting convenient parameters. Moreover, the presented results generalize several already published inequalities.

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20

Oros, Georgia Irina, Gheorghe Oros, and Shigeyoshi Owa. "Subordination Properties of Certain Operators Concerning Fractional Integral and Libera Integral Operator." Fractal and Fractional 7, no. 1 (December 30, 2022): 42. http://dx.doi.org/10.3390/fractalfract7010042.

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The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying the Libera integral operator and fractional integral of order λ for analytic functions. Many subordination properties are obtained for this newly defined operator by using famous lemmas proved by important scientists concerned with geometric function theory, such as Eenigenburg, Hallenbeck, Miller, Mocanu, Nunokawa, Reade, Ruscheweyh and Suffridge. Results regarding strong starlikeness and convexity of order α are also discussed, and an example shows how the outcome of the research can be applied.

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21

Jain, Pankaj, Sandhya Jain, and Vladimir Stepanov. "LCT BASED INTEGRAL TRANSFORMS AND HAUSDORFF OPERATORS." Eurasian Mathematical Journal 11, no. 1 (2020): 57–71. http://dx.doi.org/10.32523/2077-9879-2020-11-1-57-71.

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22

Chen, Dongyang, and Bentuo Zheng. "Lipschitz -integral operators and Lipschitz -nuclear operators." Nonlinear Analysis: Theory, Methods & Applications 75, no. 13 (September 2012): 5270–82. http://dx.doi.org/10.1016/j.na.2012.04.044.

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23

Bichegkuev, M. S. "Integral operators generated by weighted shift operators." Mathematical Notes 59, no. 3 (March 1996): 321–23. http://dx.doi.org/10.1007/bf02308546.

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24

Kermausuor, Seth, and Eze R. Nwaeze. "New Fractional Integral Inequalities via k-Atangana–Baleanu Fractional Integral Operators." Fractal and Fractional 7, no. 10 (October 8, 2023): 740. http://dx.doi.org/10.3390/fractalfract7100740.

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We propose the definitions of some fractional integral operators called k-Atangana–Baleanu fractional integral operators. These newly proposed operators are generalizations of the well-known Atangana–Baleanu fractional integral operators. As an application, we establish a generalization of the Hermite–Hadamard inequality. Additionally, we establish some new identities involving these new integral operators and obtained new fractional integral inequalities of the midpoint and trapezoidal type for functions whose derivatives are bounded or convex.

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25

Deniz, Emre, Ali Aral, and Gulsum Ulusoy. "New integral type operators." Filomat 31, no. 9 (2017): 2851–65. http://dx.doi.org/10.2298/fil1709851d.

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In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0,?).

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26

Alsalami, Omar Mutab, Soubhagya Kumar Sahoo, Muhammad Tariq, Asif Ali Shaikh, Clemente Cesarano, and Kamsing Nonlaopon. "Some New Fractional Integral Inequalities Pertaining to Generalized Fractional Integral Operator." Symmetry 14, no. 8 (August 15, 2022): 1691. http://dx.doi.org/10.3390/sym14081691.

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Integral inequalities make up a comprehensive and prolific field of research within the field of mathematical interpretations. Integral inequalities in association with convexity have a strong relationship with symmetry. Different disciplines of mathematics and applied sciences have taken a new path as a result of the development of new fractional operators. Different new fractional operators have been used to improve some mathematical inequalities and to bring new ideas in recent years. To take steps forward, we prove various Grüss-type and Chebyshev-type inequalities for integrable functions in the frame of non-conformable fractional integral operators. The key results are proven using definitions of the fractional integrals, well-known classical inequalities, and classical relations.

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27

Gül, Erdal, and Abdüllatif Yalçın. "Some integral inequalities through tempered fractional integral operator." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 2 (February 22, 2024): 399–409. http://dx.doi.org/10.31801/cfsuasmas.1387622.

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In this article, we adopt the tempered fractional integral operators to develop some novel Minkowski and Hermite-Hadamard type integral inequalities. Thus, we give several special cases of the integral inequalities for tempered fractional integrals obtained in the earlier works.

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28

Tassaddiq, Asifa, Rekha Srivastava, Rabab Alharbi, Ruhaila Md Kasmani, and Sania Qureshi. "New Inequalities Using Multiple Erdélyi–Kober Fractional Integral Operators." Fractal and Fractional 8, no. 4 (March 22, 2024): 180. http://dx.doi.org/10.3390/fractalfract8040180.

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The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to establish Minkowski fractional inequalities. Several other new and novel fractional integral inequalities are also established. Compared to the existing results, these fractional integral inequalities are more general and substantial enough to create new and novel results. M-E-K fractional integral operators have been previously applied for other purposes but have never been applied to the subject of this paper. These operators generalize a popular class of fractional integrals; therefore, this approach will open an avenue for new research. The smart properties of these operators urge us to investigate more results using them.

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29

Cabrera-Padilla, M. G., and A. Jimenez-Vargas. "Lipschitz Grothendieck-integral operators." Banach Journal of Mathematical Analysis 9, no. 4 (2015): 34–57. http://dx.doi.org/10.15352/bjma/09-4-3.

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30

Lorist, Emiel, and Mark Veraar. "Singular stochastic integral operators." Analysis & PDE 14, no. 5 (August 22, 2021): 1443–507. http://dx.doi.org/10.2140/apde.2021.14.1443.

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31

BHUSNOORMATH, SUBHAS S., and MANJUNATH V. DEVADAS. "ON SPIRALLIKE INTEGRAL OPERATORS." Tamkang Journal of Mathematics 25, no. 3 (September 1, 1994): 217–20. http://dx.doi.org/10.5556/j.tkjm.25.1994.4445.

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In this paper the integral operators \[ F(z)=\left[\frac{\beta+\gamma}{z^\gamma}\int_0^z [f(t)]^\beta t^{\gamma-1} dt\right]^{1/\beta}\] for $f(z) \in S^\alpha(\lambda, a, b)$ are studied. $S^\alpha(\lambda, a, b)$ as a subclass of the class of all spirallike functions was introduced and studied by the authors. It is shown that $F(z)$ is also in $S^\alpha(\lambda, a, b)$, whenever $f(z)$ is in $S^\alpha(\lambda, a, b)$, under certain restrictions.

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32

Gupta, Anupama. "Isometric Composite Integral Operators." Journal of Scientific Research and Reports 3, no. 9 (January 10, 2014): 1135–43. http://dx.doi.org/10.9734/jsrr/2014/8237.

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33

Labuda, Iwo. "Domains of integral operators." Studia Mathematica 111, no. 1 (1994): 53–68. http://dx.doi.org/10.4064/sm-111-1-53-68.

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34

Miller, Sanford S., and Petru T. Mocanu. "Double integral starlike operators†." Integral Transforms and Special Functions 19, no. 8 (August 2008): 591–97. http://dx.doi.org/10.1080/10652460802045282.

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35

Aleksandrov, A. B., and Vladimir V. Peller. "Distorted Hankel integral operators." Indiana University Mathematics Journal 53, no. 4 (2004): 925–40. http://dx.doi.org/10.1512/iumj.2004.53.2525.

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36

Kelley, C. T., and Z. Q. Xue. "GMRES and Integral Operators." SIAM Journal on Scientific Computing 17, no. 1 (January 1996): 217–26. http://dx.doi.org/10.1137/0917015.

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37

Al-Qassem, Hussain, and Ahmad Al-Salman. "Rough Marcinkiewicz integral operators." International Journal of Mathematics and Mathematical Sciences 27, no. 8 (2001): 495–503. http://dx.doi.org/10.1155/s0161171201006548.

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We study the Marcinkiewicz integral operatorM𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where𝒫is a polynomial mapping fromℝnintoℝdandΩis a homogeneous function of degree zero onℝnwith mean value zero over the unit sphereSn−1. We prove anLpboundedness result ofM𝒫for roughΩ.

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38

Banaś, J., and D. O'Regan. "Volterra-stieltjes integral operators." Mathematical and Computer Modelling 41, no. 2-3 (January 2005): 335–44. http://dx.doi.org/10.1016/j.mcm.2003.02.014.

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39

Cho, Yong-Kum. "Regularity of Integral Operators." Integral Equations and Operator Theory 48, no. 4 (April 1, 2004): 443–59. http://dx.doi.org/10.1007/s00020-002-1187-7.

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40

Peleshenko, B. I., and V. A. Katan. "On integral convolution operators." Mathematical Notes 66, no. 4 (October 1999): 451–54. http://dx.doi.org/10.1007/bf02679095.

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41

Gupta, Vijay. "Combinations of integral operators." Applied Mathematics and Computation 224 (November 2013): 876–81. http://dx.doi.org/10.1016/j.amc.2013.09.021.

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42

Grafakos, Loukas, and Marco M. Peloso. "Bilinear Fourier integral operators." Journal of Pseudo-Differential Operators and Applications 1, no. 2 (June 2010): 161–82. http://dx.doi.org/10.1007/s11868-010-0011-4.

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43

Iftimie, Viorel, and Radu Purice. "Magnetic Fourier integral operators." Journal of Pseudo-Differential Operators and Applications 2, no. 2 (March 18, 2011): 141–218. http://dx.doi.org/10.1007/s11868-011-0028-3.

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44

Bernal-Gonz�lez, L., M. C. Calder�n-Moreno, and K. G. Grosse-Erdmann. "Strongly omnipresent integral operators." Integral Equations and Operator Theory 44, no. 4 (December 2002): 397–409. http://dx.doi.org/10.1007/bf01193668.

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45

Labuda, Iwo, and Pawel Szeptycki. "Extensions of integral operators." Mathematische Annalen 281, no. 2 (June 1988): 341–53. http://dx.doi.org/10.1007/bf01458439.

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46

Du, Jinyuan. "SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS." Acta Mathematica Scientia 18, no. 2 (April 1998): 227–40. http://dx.doi.org/10.1016/s0252-9602(17)30757-9.

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47

Tariq, Muhammad, Sotiris K. Ntouyas, and Asif Ali Shaikh. "A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators." Axioms 12, no. 7 (July 24, 2023): 719. http://dx.doi.org/10.3390/axioms12070719.

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A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented. In the numerous families of convexities, it includes classical convex functions, s-convex functions, quasi-convex functions, strongly convex functions, harmonically convex functions, harmonically quasi-convex functions, quasi-geometrically convex functions, p-convex functions, convexity with respect to strictly monotone function, co-ordinated-convex functions, (θ,h−m)−p-convex functions, and h-preinvex functions. Included in the fractional integral operators are Riemann–Liouville fractional integral, (k−p)-Riemann–Liouville, k-Riemann–Liouville fractional integral, Riemann–Liouville fractional integrals with respect to another function, the weighted fractional integrals of a function with respect to another function, fractional integral operators with the exponential kernel, Hadamard fractional integral, Raina fractional integral operator, conformable integrals, non-conformable fractional integral, and Katugampola fractional integral. Finally, Fejér-type fractional integral inequalities for invex functions and (p,q)-calculus are also included.

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48

Srivastava, Hari Mohan, Artion Kashuri, Pshtiwan Othman Mohammed, and Kamsing Nonlaopon. "Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators." Fractal and Fractional 5, no. 4 (October 9, 2021): 160. http://dx.doi.org/10.3390/fractalfract5040160.

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In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate the Chebyshev inequality via this general family of fractional integral operators. Moreover, we derive new results of this type of inequalities for finite products of functions. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. From our above-mentioned results, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view. Furthermore, two important results and some interesting consequences for convex functions in the framework of the defined class of generalized fractional integral operators are established. Finally, two basic examples demonstrated the significance of our results.

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49

Shi, Yanlong, Li Li, and Zhonghua Shen. "Boundedness of p -Adic Singular Integrals and Multilinear Commutator on Morrey-Herz Spaces." Journal of Function Spaces 2023 (April 18, 2023): 1–11. http://dx.doi.org/10.1155/2023/9965919.

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In this paper, we establish the boundedness of classical p -adic singular integrals on Morrey-Herz spaces, as well as the boundedness of multilinear commutator generated by p -adic singular integral operators and Lipschitz functions or by p -adic singular integral operators and λ -central BMO functions.

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50

Okada, Susumu, and Yoshiaki Okazaki. "Injective absolutely summing operators." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (May 1988): 497–502. http://dx.doi.org/10.1017/s0305004100065105.

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Let X be an infinite-dimensional Banach space. It is well-known that the space of X-valued, Pettis integrable functions is not always complete with respect to the topology of convergence in mean, that is, the uniform convergence of indefinite integrals (see [14]). The Archimedes integral introduced in [9] does not suffer from this defect. For the Archimedes integral, functions to be integrated are allowed to take values in a locally convex space Y larger than the space X while X accommodates the values of indefinite integrals. Moreover, there exists a locally convex space Y, into which X is continuously embedded, such that the space ℒ(μX, Y) of Y-valued, Archimedes integrable functions is identical to the completion of the space of X valued, simple functions with repect to the toplogy of convergence in mean, for each non-negative measure μ (see [9]).

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