Abstract
In this paper, the authors introduce two new classes of generalized convexfunctions of two independent variables, and establish a new integralidentity, from which they derive some new fractional Ostrowski's integralinequalities for functions whose second derivatives are in these new classesof functions.
Highlights
The above inequality did not stop attracting the attention of researchers, various generalizations, refinements, extensions and variants have appeared in the literature see [1, 4, 11–16, 28, 29, 31, 32, 34, 37] and references therein
One of the most significant generalization is that introduced by Hanson [5] where he introduced the concept of invexity, In [3] the authors gave the notion of preinvex functions which is special case of invexity
Many authors have study the basic properties of invex set and preinvex functions, and their role in optimization, variational inequalities and equilibrium problems, see [19, 20, 30, 35, 38]
Summary
The above inequality did not stop attracting the attention of researchers, various generalizations, refinements, extensions and variants have appeared in the literature see [1, 4, 11–16, 28, 29, 31, 32, 34, 37] and references therein. [7] A function f : ∆ → R is said to be co-ordinated quasi-convex on ∆, if f (tx + (1 − t) u, λy + (1 − λ) v) ≤ max {f (x, y), f (x, v), f (u, y), f (u, v)}
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