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. That is, this study is a generalization of the definition of "$n$-polynomial convexity" previously found in the literature. 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.

Keywords

• convex function
• n-polynomial convexity
• generalized n-polynomial convexity
• Hermite-Hadamard inequality
• Hölder-İşcan integral inequality

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