New Quantum Estimates of Trapezium-Type Inequalities for Generalized <i>ϕ</i>-Convex Functions

Abstract

In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

Keywords

• hermite–hadamard inequality
• hölder’s inequality
• power mean inequality
• quantum estimates
• raina’s function
• convex function