New Integral Inequalities of the type of Sinson's and Hermite-Hadamard's for the twice Differentiable Quasi-Geometrically convex mappings

TL;DR

This paper introduces new integral inequalities for twice differentiable quasi-geometrically convex functions, extending classical inequalities like Hermite-Hadamard and Simson's, through a novel identity and estimation techniques.

Contribution

It presents a new identity for twice differentiable functions and derives generalized inequalities for quasi-geometrically convex mappings, expanding existing mathematical frameworks.

Findings

Derived new estimates for generalized Hermite-Hadamard inequalities

Extended Simson's type inequalities to quasi-geometrically convex functions

Provided a novel identity useful for analyzing twice differentiable mappings

Abstract

In this paper, we define a new identity for twice differentiable mappings and obtained some new estimates on the generalization of Hadamard's and Simson's type inequalities for quasi-geometrically convex mappings using of this identity.