On n-Polynomial convexity and some related inequalities

By Tekin Toplu, M. Kadakal, Imdat Iscan. 2020

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In this paper, we introduce and study the concept of n-polynomial convexity functions and their some algebric properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is n-polynomial convexity. Also, we compare the results obtained with both Holder, Holder-Iscan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Holder-Iscan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/be3bb656a313a119e1169d8f3d37e7af49f93618