On Some Integral Inequalities for Twice Diferentiable φ - Convex and Quasi - Convex Functions via k - Fractional Integrals
M. Esra Yildirim *
Department of Mathematics, Faculty of Science, University of Cumhuriyet, 58140, Sivas, Turkey.
Abdullah Akkurt
Department of Mathematics, Faculty of Science and Arts, University of Kahramanmaras Sütçü İmam, 46100, Kahramanmaras, Turkey.
Hüseyin Yildirim
Department of Mathematics, Faculty of Science and Arts, University of Kahramanmaras Sütçü İmam, 46100, Kahramanmaras, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, by using the integral equality which is given in this work, we aim at establishing some new inequalities of the Simpson-like and the Hadamard-like type for functions whose second derivatives are φ-convex and quasi-convex.
Keywords: h−convex functions, Quasi- convex function, Hermite-Hadamard type inequalities, Simpson's inequality, k-gamma functions, k-beta function.