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Öğe Chebyshev Type Inequalities for Generalized Stochastic Fractional Integrals(Amer Inst Physics, 2017) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Dahmani, ZoubirThe concept of comonotonic stochastic processes was introduced by Agahi and Yadollahzadeh. In this paper, we establish some Chebyshev type inequalities for comonotonic stochastic processes via generalized mean-square fractional integrals J(rho,lambda,a+;omega)(sigma) and J(rho,lambda,b-;omega)(sigma) which were introduced by Budak and Sarikaya.Öğe A COMPANION OF GENERALIZATION OF OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS OF TWO VARIABLES WITH BOUNDED VARIATION(Ministry Communications & High Technologies Republic Azerbaijan, 2016) Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this paper, a companion of generalization of Ostrowski type inequalities for functions of two variables with bounded variation is given and applications in qubature formula is provided.Öğe A companion of Ostrowski type inequalities for mappings of bounded variation and some applications(Ivane Javakhishvili Tbilisi State Univ, 2017) Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this paper, we establish a companion of Ostrowski type inequalities for mappings of bounded variation and the quadrature formula is also provided. (C) 2017 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.Öğe A Comprehensive Analysis of Hermite-Hadamard Type Inequalities via Generalized Preinvex Functions(Mdpi, 2021) Tariq, Muhammad; Ahmad, Hijaz; Budak, Hüseyin; Sahoo, Soubhagya Kumar; Sitthiwirattham, Thanin; Reunsumrit, JirapornThe principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite-Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field.Öğe Fractional Hermite-Hadamard Type Inequalities for Subadditive Functions(Univ Nis, Fac Sci Math, 2022) Ali, Muhammad Aamir; Sarıkaya, Mehmet Zeki; Budak, HüseyinIn this paper, we establish different variants of fractional Hermite-Hadamard inequalities for subadditive functions via Riemann-Liouville fractional integrals. Moreover, we offer some fractional integral inequalities for the product of two subadditive functions via Riemann-Liouville fractional integrals. It is also shown that the inequalities offered in this research are the generalization of the already given inequalities for convex functions and subadditive functions.Öğe Fractional Ostrowski type inequalities for differentiable harmonically convex functions(Amer Inst Mathematical Sciences-Aims, 2022) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Ntouyas, Sotiris K.; Promsakon, ChanonIn this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.Öğe Fractional Ostrowski Type Inequalities for Interval Valued Functions(Univ Nis, Fac Sci Math, 2022) Budak, Hüseyin; Kashuri, Artion; Butt, Saad IhsanIn this paper, we establish some generalization of Ostrowski type inequalities for interval valued functions by using the definitions of the gH-derivatives. At the end, a briefly conclusion is given as well.Öğe Further Midpoint Inequalities via Generalized Fractional Operators in Riemann-Liouville Sense(Mdpi, 2022) Hyder, Abd-Allah; Budak, Hüseyin; Almoneef, Areej A.In this study, new midpoint-type inequalities are given through recently generalized Riemann-Liouville fractional integrals. Foremost, we present an identity for a class of differentiable functions including the proposed fractional integrals. Then, several midpoint-type inequalities containing generalized Riemann-Liouville fractional integrals are proved by employing the features of convex and concave functions. Furthermore, all obtained results in this study can be compared to previously published results.Öğe A GENERALIZED AND REFINED PERTURBED VERSION OF OSTROWSKI TYPE INEQUALITIES(Etamaths Publ, 2017) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Erden, Samet; Qayyum, AtherIn this paper, we first obtain a new identity for twice differentiable mappings. Then, we establish generalized and improved perturbed version of Ostrowski type inequalities for functions whose derivatives are of bounded variation or second derivatives are either bounded or Lipschitzian.Öğe Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions(De Gruyter Poland Sp Z O O, 2022) Vivas-Cortez, Miguel J. J.; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Chasreechai, SaowaluckIn this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.Öğe Generalized fractional midpoint type inequalities for co-ordinated convex functions(University of Nis, 2023) Hezenci, Fatih; Budak, Hüseyin; Kara, Hasan; Sarıkaya, Mehmet ZekiIn this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results. © 2023, University of Nis. All rights reserved.Öğe Generalized Hermite - Hadamard Type Integral Inequalities for Fractional Integrals(Univ Nis, Fac Sci Math, 2016) Sarıkaya, Mehmet Zeki; Budak, HüseyinIn this paper, we have established Hermite-Hadamard type inequalities for fractional integrals depending on a parameter.Öğe Generalized Midpoint Fractional Integral Inequalities via h-Convexity(Univ Nis, Fac Sci Math, 2021) Mahreen, Kahkashan; Budak, HüseyinIn this research, generalizations of midpoint type inequalities are established. h-convexity is used as a tool. These inequalities are for differentiable functions which involve Riemann-Liouville fractional integrals. Also, some consequences of these established inequalities are obtained.Öğe GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES ARE GENERALIZED s-CONVEX IN THE SECOND SENSE(Czestochowa Univ Technology, Inst Mathematics, 2016) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Set, ErhanIn this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.Öğe GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS(Amer Mathematical Soc, 2017) Sarıkaya, Mehmet Zeki; Budak, HüseyinFirst, we establish the generalized Ostrowski inequality for local fractional integrals on fractal sets R-alpha (0 < alpha <= 1) of real line numbers. Secondly, we obtain some new inequalities using the generalized convex function on fractal sets R-alpha.Öğe Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals(Springer-Verlag Italia Srl, 2017) Akkurt, Abdullah; Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Yıldırım, HüseyinIn this paper, we obtain generalized Ostrowski type integral inequalities involving moments of a continuous random variables via local fractional integrals.Öğe Generalized p-Convex Fuzzy-Interval-Valued Functions and Inequalities Based upon the Fuzzy-Order Relation(Mdpi, 2022) Khan, Muhammad Bilal; Treanta, Savin; Budak, HüseyinConvexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p,s)-convex fuzzy interval-valued functions ((p,s)-convex F-I-V-Fs) in the second sense and to establish Hermite-Hadamard (H-H) type inequalities for (p,s)-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for (p,s)-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.Öğe GENERALIZED QUANTUM MONTGOMERY IDENTITY AND OSTROWSKI TYPE INEQUALITIES FOR PREINVEX FUNCTIONS(Inst Applied Mathematics, 2022) Kalsoom, Humaira; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hüseyin; MURTAZA, GHULAMIn this research, we give a generalized version of the quantum Montgomery identity using the quantum integral. We establish some new inequalities of Ostrowski type by means of newly derived identity. Moreover, we consider the special cases of the newly obtained results and prove several new and known Ostrowski and midpoint inequalities.Öğe GENERALIZED WEIGHTED CEBYSEV AND OSTROWSKI TYPE INEQUALITIES FOR DOUBLE INTEGRALS(Turkic World Mathematical Soc, 2017) Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this paper, we firstly establish generalized weighted Montgomery identity for double integrals. Then, some generalized weighted Cebysev and Ostrowski type inequalities for double integrals are given.Öğe Gruss type inequalities for generalized fractional integrals(Amer Inst Physics, 2016) Erden, Samet; Sarıkaya, Mehmet Zeki; Budak, HüseyinIn this study, some Gruss type inequalities for generalized fractional integrals are presented. Also, the results presented here would provide extensions of those given in earlier works.
