On Generalization of Trapezoid Type Inequalities for <i>s</i>-Convex Functions with Generalized Fractional Integral Operators

Usta F., Budak H., Sarikaya M. Z., Set E.

FILOMAT, no.6, pp.2153-2171, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1806153u
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2153-2171
  • Kocaeli University Affiliated: No

Abstract

By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite Hadamard's type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where vertical bar f'vertical bar and vertical bar f ''vertical bar (or vertical bar f'vertical bar(q) and vertical bar f ''vertical bar(q) for q >= 1) are s-convex hold by applying the Holder inequality and the power mean inequality.