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On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals

Journal: Sahand Communications in Mathematical Analysis (Vol.19, No. 2)

Publication Date:

Authors : ; ; ;

Page : 65-79

Keywords : Hermite-Hadamard inequality; convex function; Bounded function;

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Abstract

In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $phi (x)=varpi left( frac{kappa _{1}kappa _{2}}{mathcal{varkappa }}right)  $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $phi ^{prime }left( kappa_{1}+kappa _{2}-mathcal{varkappa }right) geq phi ^{prime }(mathcal{varkappa })$ instead of harmonically convexity of $varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results.

Last modified: 2022-07-31 17:27:17