Multi-Parameter Quantum Integral Identity Involving Raina’s Function and Corresponding <i>q</i>-Integral Inequalities with Applications

Abstract

Convexity performs its due role in the theoretical field of inequalities according to the nature and conduct of the properties it displays. A correlation connectivity, which is visible between the two variables symmetry and convexity, enhances its importance. In this paper, we derive a new multi-parameter quantum integral identity involving Raina’s function. Applying this generic identity as an auxiliary result, we establish some new generalized quantum estimates of certain integral inequalities pertaining to the class of Rs-convex functions. Moreover, we give quantum integral inequalities for the product of Rs1- and Rs2-convex functions as well as another quantum result for a function that satisfies a special condition. In order to demonstrate the efficiency of our main results, we offer many important special cases for suitable choices of parameters and finally for Rs-convex functions that are absolute-value bounded.

Keywords

• convexity
• Rs-convex
• quantum derivatives
• quantum integrals
• Hölder’s inequality