Some New Ostrowski Type Inequalities Concerning Differentiable Generalized Relative Semi-(r; m, p, q, h₁, h₂)-Preinvex Mappings

Artion Kashuri^1, , Rozana Liko¹ and Tingsong Du²

¹Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, Vlora, Albania

²College of Science, China Three Gorges University, 443002, Yichang, P. R. China

Cite this paper:
Artion Kashuri, Rozana Liko and Tingsong Du. Some New Ostrowski Type Inequalities Concerning Differentiable Generalized Relative Semi-(r; m, p, q, h₁, h₂)-Preinvex Mappings. Turkish Journal of Analysis and Number Theory. 2018; 6(1):16-29. doi: 10.12691/tjant-6-1-3

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.

Keywords:
Ostrowski type inequality Hölder's inequality Minkowski inequality power mean inequality m-invex.

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