Abstract
In this article, we first presented a new integral identity concerning differentiable mappings defined on m-invex sets. By using the notion of generalized relative semi-(r; m, p, q, h1, h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Ostrowski type inequalities are established. It is pointed out that some new special cases can be deduced from main results of the article.
Highlights
The subsequent inequality is known as Ostrowski inequality which gives an upper bound for the approximation of the integral average b 1 − a∫ ab f (t )dt by the value f ( x) at point x ∈[a,b].Theorem 1.1
Motivated by the above literatures, the main objective of this article is to establish some new estimates on generalizations of Ostrowski type inequalities associated with differentiable generalized relative semi-(r; m, p, q, h1, h2) -preinvex mappings on m-invex sets
Using our Theorems 2.7 and 2.14 for different values of α, k, m, p1, p2, for some suitable continuous functions h1, h2, φ and complex numbers λ1 ( x), λ2 ( x), we can get some new Ostrowski type inequalities associated with generalized relative semi-(r; m, p1, p2, h1, h2)-preinvex mappings
Summary
The subsequent inequality is known as Ostrowski inequality which gives an upper bound for the approximation of the integral average b 1 − a∫ ab f (t )dt by the value f ( x) at point x ∈[a,b].Theorem 1.1. Let see the following example of a generalized relative semi-(r; m, p, q, h1, h2)-preinvex mappings which is not convex.
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