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

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.

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