Quantum integral inequalities for generalized preinvex functions

Abstract

We consider the generalized preinvex functions, which unify the preinvex and φ-convex functions. We give an account of the quantum integral inequalities via the generalized preinvex functions. Results obtained in this chapter represent significant and important refinements of the known results. These inequalities involve Riemann-type quantum integrals. We would like to emphasize that these results reduce to classical results, when q → 1. It is expected that ideas and techniques given here would inspire further research.