On Geodesic Semi E-b-Preinvex Functions

Abstract

In this paper, we introduce and investigate a novel class of functions termed as geodesic semi E-b-preinvex (GSEBPI) functions on RMs (Riemannian manifolds). These functions are defined on geodesic E-b-invex (GEBI) sets with respect to a mapping  ,  there by extending existing generalized convexity concepts within a geometric framework. Several fundamental properties and structural characterizations are established, along with connections to related convexity notions. Further, we consider the non-linear programming problems and prove some results by using GEBPI, GSEBPI, strictly GSEBPI, GQSEBPI functions for optimality. At the end of this paper, it is shown that, under appropriate differentiability assumptions, every GEBI functions is GEBPI functions. The results contribute to the advancement of geometric optimization and nonlinear analysis on RMs.