Generalized (p,q)-analogues of Dragomir-Agarwal's inequalities involving Raina's function and applications

Abstract

In this paper, we introduce the class of generalized strongly convex functions using Raina's function. We derive two new general auxiliary results involving first and second order (p,q)-differentiable functions and Raina's function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal's inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p,q)-differentiable functions of first and second order that are bounded in absolute value.

Keywords

• dragomir-agarwal's inequality
• hölder inequality
• power-mean inequality
• generalized strongly convex functions
• raina's function
• post-quantum calculus