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

Creative Commons License

İşcan İ.

Miskolc Mathematical Notes, cilt.24, sa.3, ss.1389-1404, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.18514/mmn.2023.4142
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.1389-1404
  • Anahtar Kelimeler: convex function, Hermite-Hadamard inequality, Hölder integral inequality, Hölder-İşcan integral inequality, n-fractional polynomial convexity
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Karadeniz Teknik Üniversitesi Adresli: Hayır

Özet

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.