Some properties of geodesic $(\alpha,E)$-preinvex functions on Riemannian manifolds

Document Type : Original Article

Authors

Absos Ali Shaikh ¹

Chandan Kumar Mondal ¹

Ravi P. Agarwal ²

¹ University of Burdwan

² Department of Mathematics, Texas A&M University, Texas

10.22034/kjm.2020.220226.1717

Abstract

In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$-invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic $(\alpha,E)$-invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic $(\alpha,E)$-invex set. We have also established an important relation between geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex function in a complete Riemannian manifold.

Keywords

Invex sets

Invex functions

Geodesic Preinvex functions

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