Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus

Abstract

In this paper, firstly we research basic definition of convexity in terms of non-Newtonian calculi, i.e. interval, convex set, convexity, etc. Secondly, we deal with the different classes of convexity and generalizations via non-Newtonian calculi. Finally, we reveal the new generalization of the definition of convexity that can reduce many order of convexity and constitute some new Hermite-Hadamard type inequalities for this calculi.