Construction of a new generalization for n-polynomial convexity with their certain inequalities

Abstract

In this paper, we first construct a new generalization of n-polynomial convex function. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n polynomial convexity. Also, we see that the obtained results in the paper while comparing with Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.