CONSTRUCTION OF A NEW CLASS OF FUNCTIONS WITH THEIR SOME PROPERTIES AND CERTAIN INEQUALITIES: n-FRACTIONAL POLYNOMIAL CONVEX FUNCTIONS

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İşcan İ.

Miskolc Mathematical Notes, vol.24, no.3, pp.1389-1404, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.18514/mmn.2023.4142
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.1389-1404
  • Keywords: convex function, Hermite-Hadamard inequality, Hölder integral inequality, Hölder-İşcan integral inequality, n-fractional polynomial convexity
  • Karadeniz Technical University Affiliated: No

Abstract

In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. 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.