Semi P-geometric-arithmetically functions and some new related inequalities

Kadakal M., İşcan İ., Kadakal H.

Filomat, vol.37, no.21, pp.7017-7028, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 21
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2321017k
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.7017-7028
  • Keywords: Subject Classification, Convex function, semi P-function, semi P-GA function, Hermite-Hadamard can, HERMITE-HADAMARD TYPE
  • Karadeniz Technical University Affiliated: No

Abstract

In this manuscript, the authors introduce the concept of the semi P-geometric–arithmetically functions (semi P-GA functions) and give their some algebraic properties. Then, they get Hermite-Hadamard’s integral inequalities for semi P-GA-functions (geometric-arithmetically convex). In addition, the authors obtain new inequalities by using Hölder and Hölder-İşcan integral inequalities with the help of an identity. Then, the aouthors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.