On generalization of midpoint type inequalities with generalized fractional integral operators (original) (raw)
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Filomat, 2018
By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite-Hadamard?s type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where |f'| and |f''| (or |f'|q and |f''|q for q ? 1) are s-convex hold by applying the H?lder inequality and the power mean inequality.
New generalization of Hermite-Hadamard type inequalities via generalized fractional integrals
Annals of the University of Craiova - Mathematics and Computer Science Series, 2020
In this paper we obtain new generalization of Hermite-Hadamard inequalities via generalized fractional integrals defined by Sarikaya and Ertugral. We establish some midpoint and trapezoid type inequalities for functions whose first derivatives in absolute value are convex involving generalized fractional integrals.
Journal of Mathematical Inequalities
In this research article, authors have established a general integral identity for Riemann-Liouville fractional integrals. Some new results related to the left-hand side of Hermite-Hadamard type integral inequalities utilizing this integral identity for the class of functions whose second derivatives at some power are P-convex are obtained.The presented results have some closely connection with [M. E.Özdemir, C. Yıldız, A. O. Akdemir, E. Set, On some inequalities for s-convex functions and applications, Jounal of Inequalities and Applications, 2013:333]