TY - JOUR ID - 239415 TI - On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Budak, Huseyin AU - Pehlivan, Ebru AU - Kosem, Pınar AD - Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey Y1 - 2021 PY - 2021 VL - 18 IS - 1 SP - 73 EP - 88 KW - Hermite-Hadamard inequality KW - convex function KW - Bounded function DO - 10.22130/scma.2020.121963.759 N2 - In 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. UR - https://scma.maragheh.ac.ir/article_239415.html L1 - https://scma.maragheh.ac.ir/article_239415_dfab209b0c7827293020ea7826eca758.pdf ER -