Abstract: We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.

Key words: generalized convex spaces, weakly G-quasiconvex map, KKM map, Γ-convex; u.s.c., l.s.c., almost ?xed point