Several integral inequalities for (alpha, s, m) -convex functions


Ozdemir M. E. , Butt S., BAYRAKTAR B., Nasir J.

AIMS MATHEMATICS, vol.5, no.4, pp.3906-3921, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3934/math.2020253
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3906-3921
  • Keywords: convex function, (alpha, s, m)-convex function, Hermite-Hadamard inequality, Riemann-Liouville fractional integrals, Holder's inequality, power mean inequality, Psi-Gamma functions, HERMITE-HADAMARD-TYPE, M)-CONVEX, (ALPHA, (S
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we establish several new integral inequalities for (alpha, s, m)-convex functions. We recapture the Hermite-Hadamard inequality as a particular case. In order to obtain our results, we use classical inequalities such as Holder inequality, Holder-Iscan inequality and Power mean inequality. We formulate several bounds involving special functions like classical Euler-Gamma, Beta and Psi-Gamma functions. We also give some applications.