%0 Journal Article
%T On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Budak, Huseyin
%A Can Bilişik, Candan
%A Sarikaya, Mehmet Zeki
%D 2022
%\ 06/01/2022
%V 19
%N 2
%P 65-79
%! On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
%K Hermite-Hadamard inequality
%K convex function
%K Bounded function
%R 10.22130/scma.2022.539417.992
%X 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.
%U https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdf