AIMS Mathematics (Jan 2020)

On <em>n</em>-Polynomial convexity and some related inequalities

  • Tekin Toplu,
  • Mahir Kadakal,
  • İmdat İşcan

DOI
https://doi.org/10.3934/math.2020089
Journal volume & issue
Vol. 5, no. 2
pp. 1304 – 1318

Abstract

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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 Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given.

Keywords