Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals

Abstract

In the present research, we develop some integral inequalities of Hermite-Hadamard type for differentiable η-convex functions. Moreover, our results include several new and known results as particular cases.

Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

“…e works above can also build up for a convex function of two variables. For further directions, we refer to [28][29][30][31][32][33].…”

Inequalities for Unified Integral Operators via Stronglyα,h‐m-Convexity

“…They are extended and generalized in different ways to obtain corresponding generalizations and extensions of well-known inequalities. For the detail study of different kinds of convex functions, we refer the readers to [1][2][3][4][5][6][7].…”

On Generalized Strongly p-Convex Functions of Higher Order

“…Since the convexity of sets and functions has been the main object of studies of recent years, in many new problems encountered in applied mathematics, the notion of classical convexity is not enough to reach favorite results [1][2][3][4]. Recently, several extensions have been considered for classical convexity such that some of these new concepts are based on extension of the domain of convex function or set to a generalized form [5][6][7]. Some new generalized concepts in this point of view are pseudoconvex function, quasiconvex functions, invex functions, preinvex functions, B-convex functions, strongly convex functions, and generalized strongly convex functions.…”