The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.

In this paper, with the aid of idea of defining those sets and functions, the definitions of E -convex cone, pseudo-quasi- E -convex functions, E -direction derivative are discussed.

This paper discusses the relationship between quasi-concave and pseudo-convex in the generalized convex function in the Linear topological space and offers some conditions of equivalence.