Some Integral Inequalities for h-Godunova-Levin Preinvexity

Abstract

In this study, we define new classes of convexity called h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type are established. These new classes are the generalization of several known convexities including the s-convex, P-function, and Godunova-Levin. Further, the properties of the h-Godunova-Levin function are also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given.

Hermite–Hadamard and Jensen‐Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions

“…As well, Zhao et al provide a new Hermite-Hadamard inequality for h-convex functions in the context of interval-valued functions (see [23]). e following inequality was proved in 2019 by Almutairi and Kiliman using the h-Godunova-Levin function (see [24]).…”

Generalized Hermite–Hadamard-Type Integral Inequalities forh-Godunova–Levin Functions

“…e h-convexity was introduced by Varosȃnec in [34]. Ohud Almutari introduced h-Godunova-Levin convexity and h-Godunova-Levin preinvexity [35] by combining the concepts of Dragomir and Varosȃnec. In this study, we have considered h-Godunova-Levin convex and h-Godunova-Levin preinvex function to obtain generalized fractional version of Hermite-Hadamard-type inequality and trapezoid-type inequalities related to Hermite-Hadamard inequality.…”

“…Definition 5 (see [35]). Suppose h: (0, 1) ⟶ R. A nonnegative function Θ: J ⟶ R is said to be h-Godunova-Levin, for all u, v ∈ J and δ ∈ (0, 1), if…”

Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

“…The H-H inequality plays essential roles in different areas of sciences, such as mathematics, physics and engineering (for example see [3,12,32,27,25]). This inequality provides estimates for the mean value of a continuous convex function.…”