Trapezoidal type inequalities related to h-convex functions with applications

TL;DR

This paper develops new trapezoidal inequalities for h-convex functions, extending Fejer inequalities, and applies these results to special means, random variables, and numerical integration.

Contribution

It introduces a novel trapezoidal form of Fejer inequality for h-convex functions and explores their applications in various mathematical contexts.

Findings

Derived new trapezoidal inequalities for h-convex functions

Extended Fejer inequality in the context of h-convexity

Applied inequalities to special means, random variables, and trapezoidal rule

Abstract

A mapping M(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection with special means, random variable and trapezoidal formula.