University of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals738823941510.22130/scma.2020.121963.759ENHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey0000-0001-8843-955XEbruPehlivanDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, TurkeyPÄ±narKosemDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, TurkeyJournal Article20200220In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{\prime }(a+b-x)\geq f^{\prime }(x)$ for all $x\in \left[ a,\frac{a+b}{2}\right] $ instead of convexity.https://scma.maragheh.ac.ir/article_239415_3352d66ff13ca0aaf786ddd8dec3bac3.pdf