New generalization of geodesic convex function

TL;DR

This paper introduces the concept of geodesic φ_E-convex functions, extending the idea of geodesic functions, and explores their properties, sets, epigraphs, and characterizations.

Contribution

It presents a new generalization of geodesic convex functions called geodesic φ_E-convex functions, along with their properties and characterizations.

Findings

Defined geodesic φ_E-convex functions and sets

Established properties of these functions

Characterized functions via their φ_E-epigraphs

Abstract

As a generalization of geodesic function, this paper introduces the notion of geodesic $ \varphi_{E} $-convex function. Some properties of $ \varphi_{E} $-convex function and geodesic $ \varphi_{E} $-convex function are established. The concepts of geodesic $ \varphi_{E} $-convex set and $ \varphi_{E} $-epigraph are equally given. The characterization of geodesic $ \varphi_{E} $-convex functions in terms of their $ \varphi_{E} $-epigraphs are also obtained.