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Öğe FRACTIONAL OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS OF BOUNDED VARIATON WITH TWO VARIABLES(Univ Miskolc Inst Math, 2020) Erden, S.; Budak, H.; Sarikaya, M. Z.We first establish some fractional equalities for functions of bounded variation with two variables. Then we derive some fractional Ostrowski and Trapezoid type inequalities for functions of bounded variation with two variables. In addition, we give some Midpoint inequalities as special cases of our main results.Öğe Generalization of some hardy-type integral inequality with negative parameter(Transilvania University of Brasov 1, 2020) Benaissa, B.; Sarikaya, M. Z.In 2007, Bicheng Yang [3] presented a new Hardy-type integral inequality with a best constant factor. The aim of this work is to give a direct generalization of these inequalities obtained with negative parameter p < 0. © 2020, Transilvania University of Brasov 1. All rights reserved.Öğe Generalized bullen type inequalities for local fractional integrals and its applications(Palestine Polytechnic University, 2020) Erden, S.; Sarikaya, M. Z.; Lopez-Bonilla, J. L.In this paper, we establish the generalized Bullen type inequalities involving local fractional integrals on fractal sets R? (0 < ? ? 1) of real line numbers. Some applications of these inequalities in numerical integration and for special means are given. © Palestine Polytechnic University-PPU 2020.Öğe Generalized fractional hermite-hadamard type inequalities for convex functions(Natural Sciences Publishing, 2020) Budak, H.; Ali, M. A.; Sarikaya, M. Z.In this article, we obtain some Hermite-Hadamard type inequalities for differentiable convex functions involving generalized fractional integrals. Some of our results are the extension of previously obtained results like (Dragomir and Agarwal in Appl. Math. Lett. 11(5): 91-95, 1998, Dragomir, Chob and Kimc in J. Math. Anal. Appl. 245(2):489-501, 2000, Yang, H. Wang and Tseng in Comput. Math. Appl. 47(2-3):207-216, 2004 and S. Qaisar et al. in J. Inequal. Appl. 2019(1):111, 2019). We also discuss some special cases. © 2020 NSP Natural Sciences Publishing Cor.Öğe Hermite-Hadamard Type Inequalities for h-Convex Functions Via Generalized Fractional Integrals(Islamic Azad Univ, Shiraz Branch, 2020) Ali, M. Aamir; Budak, H.; Abbas, M.; Sarikaya, M. Z.; Kashuri, A.The purpose of this paper is to establish some Hermite-Hadamard type inequalities for h-convex functions utilizing generalized fractional integrals. We also obtain some generalized trapezoid and midpoint type inequalities for the mapping whose first derivatives absolutely value are h-convex. The results proved in this paper generalize the several inequalities obtained earlier worksÖğe NEW EXTENSIONS OF THE HERMITE-HADAMARD INEQUALITIES INVOLVING RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS(Univ Miskolc Inst Math, 2020) Budak, H.; Kara, H.; Sarikaya, M. Z.; Kiris, M. E.In this study, we establish the above and below bounds for the left and right hand sides of fractional Hermite-Hadamard inequalities by using functions whose second derivatives are bounded. We also give some refinements of fractional Hermite-Hadamard inequalities by using the functions that have the conditions f'(a + b - t) - f'(t) >= 0, t is an element of [a, a+b/2].Öğe New inequalities of Hermite-Hadamard type for h-convex functions via generalized fractional integrals(Natural Sciences Publishing, 2021) Ali, M. A.; Budak, H.; Sarikaya, M. Z.In this paper, we establish new inequalities of Hermite-Hadamard type for h-convex functions using generalized fractional integral. The results are an extension of a previous research © 2021. NSP Natural Sciences Publishing CorÖğe New mixed operators for fractional integrations with some applications(Cambridge Scientific Publishers, 2021) Bezziou, M.; Dahmani, Z.; Sarikaya, M. Z.; Jebril, I.In this paper, we introduce new mixed operators related to the coupled orders Riemann-Liouville integrals. Then, we prove some of their properties, such as semigroup and commutativity. At the end, some applications are discussed. © CSP - Cambridge, UK; I&S - Florida, USA, 2021Öğe NEW REFINEMENTS AND APPLICATIONS OF OSTROWSKI TYPE INEQUALITIES FOR MAPPINGS WHOSE nth DERIVATIVES ARE OF BOUNDED VARIATION(Turkic World Mathematical Soc, 2021) Budak, H.; Sarikaya, M. Z.; Qayyum, A.The main aim of this paper is to establish some Ostrowski type integral inequalities using a newly developed special type of kernel for mappings whose nth derivatives are of bounded variation. We deduce some previous results as a special case. Some new efficient quadrature rules are also introduced.Öğe On generalized the conformable fractional calculus(Isik University, 2019) Sarikaya, M. Z.; Budak, H.; Usta, F.In this paper, we generalize the conformable fractional derivative and integral and obtain several results such as the product rule, quotient rule, chain rule. © Işık University, Department of Mathematics, 2019; all rights reserved.Öğe ON REFINEMENTS of HERMITE–HADAMARD TYPE INEQUALITIES with GENERALIZED FRACTIONAL INTEGRAL OPERATORS(Element D.O.O., 2021) Budak, H.; Sarikaya, M. Z.In this paper we establish the refinements of Hermite-Hadamard type inequalities for generalized fractional integral operator through the instrument of convex functions. © 2021 Asian Journal of Dairy and Food Research. All rights reserved.Öğe ON THE HERMITE-HADAMARD TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATOR(Univ Kragujevac, Fac Science, 2020) Yaldiz, H.; Sarikaya, M. Z.In this paper, using a general class of fractional integral operators, we establish new fractional integral inequalities of Hermite-Hadamard type. The main results are used to derive Hermite-Hadamard type inequalities involving the familiar Riemann-Liouville fractional integral operators.Öğe Pompeiu type inequalities using conformable fractional calculus and its applications(Yarmouk University, 2021) Erden, S.; Sarikaya, M. Z.We establish Pompeiu's mean value theorem for ?-fractional differentiable mappings. Then, some Pompeiu type inequalities including conformable fractional integrals are obtained, and the weighted versions of this Pompeiu type inequalities are presented. Finally, some applications for quadrature rules and special means are given. © 2021 Yarmouk University. All rights reserved.Öğe Some generalizations of opial type inequalities(Natural Sciences Publishing, 2020) Sarikaya, M. Z.; Bilisik, C. C.; Mohammed, P. O.In this study, we establish some new n-th order integral inequalities of Opial type for differentiable functions. Furthermore, we extend our study by examining more general type of differentiable functions. Finally, we see that our results can cover the previous published studies. © 2020 NSP Natural Sciences Publishing Cor.Öğe Some generalizations of Opial type inequalities for conformable fractional integrals(Natural Sciences Publishing, 2020) Sarikaya, M. Z.; Bilisik, C. C.In the present paper, some new versions of Opial type inequalities for conformable fractional integral are given by using convex functions. © 2020 NSP Natural Sciences Publishing Cor.Öğe SOME GENERALIZED INTEGRAL INEQUALITIES VIA FRACTIONAL INTEGRALS(Comenius Univ, 2020) Sarikaya, M. Z.; Budak, H.; Usta, F.The main goal of this paper is to introduce a new integral definition concerned with fractional calculus. Then we establish generalized Hermite-Hadamard type integral inequalities for convex function using proposed fractional integrals. The results presented in this paper provide extensions of those given in earlier works.
