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

## TL;DR

This paper introduces and studies geodesic $(eta,E)$-preinvex functions on Riemannian manifolds, establishing their properties, relations, and providing illustrative examples to advance the understanding of generalized convexity in geometric analysis.

## Contribution

It defines geodesic $(eta,E)$-preinvex functions and explores their properties and relationships with invex functions on Riemannian manifolds, including illustrative examples.

## Key findings

- Defined geodesic $(eta,E)$-preinvex sets and functions
- Established properties and relations between preinvex and invex functions
- Provided an example illustrating the concepts

## 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.