Generalized fractional Hermite-Hadamard inequalities for twice differentiable s-convex functions

Abstract

Some Hermite-Hadamard type inequalities via Riemann-Liouville fractional integral for twice differentiable functions having some s-convexity of second kind properties are established. A class of s-affine of second kind functions is identified such as these inequalities are sharp.

On some fractional Hermite–Hadamard inequalities via s-convex and s-Godunova–Levin functions and their applications

“…According to the similar methods of the references [7,12], one can prove that if s ∈ (0, 1] then the inequalities in Theorems 3.2, 3.3, 3.6, 3.8, 3.9, 3.11, 3.12, and 3.13…”

Some new bounds for Simpson's rule involving special functions via harmonic h-convexity

“…The strong relationship between theory of convexity and theory of inequalities has attracted many researchers, as a result number classical inequalities which were obtained for convex functions have also been extended for other generalizations of convex functions, see [1,2,5,7,10,11,[13][14][15][16][17][18][19]22]. Inspired by the ongoing research, in this paper we consider the class of harmonic h-convex functions and obtain some new Simpson type inequalities.…”

Fractional Hermite–Hadamard type inequalities for interval-valued functions

“…With the increasing importance of fractional integrals, several authors extend their research by combining Hermite-Hadamard type inequalities with fractional integrals. In this way, some fractional Hermite-Hadamard type inequalities have been established, see [9][10][11][12][13][14][15] and the references therein.…”