On Novel Extension of n-Polynomial Pre-invex Functions and Related Post-Quantum Integral Inequalities with Application

Abstract

In this paper, we introduce a new class of n-polynomial pre-invex functions to investigate the refined bounds of Hermite-Hadamard type inequalities involving post-quantum integrals. We establish an advanced and comprehensive multi-parameter identity and several post-quantum integrals to aid our main results. By applying this generic identity, we estimate the unique and sharp bounds for the functions, which are bounded and satisfy the Lipschitz condition. In order to find the optimal bounds, we  examine these results for the best choice of parameters involved and express those graphically to validate our results. In the end, we calculate certain special means as the application of presented results.