On slack 2-geodesic convex set and geodesic E-pseudoconvex function with application

Abstract

We introduce a new class of sets named, slack 2-geodesic convex set on Riemannian manifolds and verify by a nontrivial example. We define a geodesic E -pseudoconvex function with a suitable example. Some properties of geodesic E -quasiconvex function are discussed. We establish some relationships between slack 2-geodesic convex set, geodesic E -pseudoconvex function and geodesic E -quasiconvex function. Moreover, an application of geodesic E -quasiconvex function to a nonlinear programming problem is also presented.