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Öğe Approximating the Finite Mellin and Sumudu Transforms Utilizing Wavelet Transform(Univ Nis, Fac Sci Math, 2020) Usta, Fuat; Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this study, some approximates for the finite Wavelet transform of different classes of absolutely continues mappings are presented using Wavelet transform of unit function. Then, with the help of these approximates, some other approximates for the finite Mellin and Sumudu transforms are given.Öğe Certain fractional inequalities via the Caputo Fabrizio operator(Univ Nis, Fac Sci Math, 2023) Qaisar, Shahid; Munir, Arslan; Budak, HüseyinThe Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadamard inequalities within a Caputo Fabrizio fractional integral framework. The fractional integral under investigation is used to establish some new fractional Hermite-Hadamard inequalities. The findings of this study can be seen as a generalization and extension of numerous earlier inequalities via convex function. In addition, we demonstrate a few applications of our findings to special means of real numbers.Öğe Certain Simpson-type inequalities for twice-differentiable functions by conformable fractional integrals(Kangwon-Kyungki Mathematical Soc, 2023) Hezenci, Fatih; Budak, HüseyinIn this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Fur-thermore, our results are provided by using special cases of obtained theorems.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 A comprehensive study on Milne-type inequalities with tempered fractional integrals(Springer, 2024) Haider, Wali; Budak, Hüseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, HaiboIn the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.Öğe Conformable fractional versions of Hermite-Hadamard-type inequalities for twice-differentiable functions(Springer, 2023) Hezenci, Fatih; Kara, Hasan; Budak, HüseyinIn this paper, new inequalities for the left and right sides of the Hermite-Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems.Öğe Deriving weighted Newton-type inequalities for diverse function classes through Riemann-Liouville fractional integrals(Pergamon-Elsevier Science Ltd, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, HüseyinThis study introduces weighted Newton-type inequalities for diverse function classes via Riemann-Liouville fractional integrals. We begin by employing a positive weighted function to demonstrate a crucial integral equality which necessary for establishing the main outcomes. Leveraging this equality along with Riemann- Liouville fractional integrals, we prove several weighted Newton-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. From the obtained results, one can get an insights into the implications of Newton-type inequalities and outlines potential avenues for future research endeavors.Öğe Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities(Amer Inst Mathematical Sciences-Aims, 2023) Budak, Hüseyin; Hyder, Abd-AllahIn this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.Öğe Error Bounds for Fractional Integral Inequalities with Applications(Mdpi, 2024) Alqahtani, Nouf Abdulrahman; Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, HüseyinFractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite-Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo-Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite-Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.Öğe Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional integrals(Springer, 2021) You, Xue-Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Agarwal, Praveen; Chu, Yu-MingIn the paper, the authors establish some new Hermite-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite-Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.Öğe An extensive study on parameterized inequalities for conformable fractional integrals(Springer Basel Ag, 2023) Hezenci, Fatih; Budak, HüseyinThis paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems.Öğe Fractional Euler-Maclaurin-type inequalities for various function classes(Springer Heidelberg, 2024) Hezenci, Fatih; Budak, HüseyinThis paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation.Öğe Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions(Univ Miskolc Inst Math, 2023) Ali, Muhammad Aamir; Soontharanon, Jarunee; Budak, Hüseyin; Sitthiwirattham, Thanin; Feckan, MichalIn this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Ho & BULL;lder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.Öğe Fractional Hermite-Hadamard inequality, Simpson's and Ostrowski's type inequalities for convex functions with respect to a pair of functions(Rocky Mt Math Consortium, 2023) Xie, Jianqiang; Ali, Muhammad Aamir; Budak, Hüseyin; Feckan, Michal; Sitthiwirattham, ThaninWe consider the convexity with respect to a pair of functions and establish a Hermite-Hadamard type inequality for Riemann-Liouville fractional integrals. Moreover, we derive some new Simpson's and Ostrowski's type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.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 Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions(De Gruyter Open Ltd, 2021) Budak, Hüseyin; Kara, H.; Ali, M. A.; Khan, S.; Chu, Y.In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by applying the newly defined fractional integrals. The results of the present paper are the extension of several previously published results. © 2021 Huseyin Budak et al., published by De Gruyter.Öğe FRACTIONAL HERMITE-HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS(Amer Mathematical Soc, 2020) Budak, Hüseyin; Tunc, Tuba; Sarıkaya, Mehmet ZekiIn this paper, we define interval-valued right-sided Riemann-Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals.
