On Ostrowski-Type Inequalities via Strong s-Godunova-Levin Functions

Authors : Badreddine Meftah, Assia Azaizia

Pages : 1-11

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Publication Date : 2021-03-30

Article Type : Research

Abstract :In this paper, we first introduce a new class of convex functions called strong s-Godunova-Levin functions, which encompass the strong Godunova-Levin, s-Godunova-Levin, and Godunova-Levin function classes. By relying on the identity given by Cerone et al. [Ostrowski-type Inequalities for Functions Whose Derivatives Satisfy Certain Convexity Assumptions, Demonstratio Mathematica 37(2) (2004) 299-308] and by some simple technical methods, we derive some new Ostrowski-type inequalities for functions whose derivatives in absolute value at a certain power q ≥ 1 lies in the above-cited new class of functions. Some special cases are discussed. The results obtained can be considered a generalization of certain known results.
Keywords : Ostrowski inequality, power mean inequality, Hölder inequality, strong s-Godunova-Levin functions