Coincidence and Maximal Element Theorems in Abstract Convex Spaces with Applications

Abstract

In this paper, by using a nonempty intersection lemma due to the authors, we obtain two coincidence theorems involved $\mathfrak{RC}$-maps in abstract convex spaces, which are actually equivalent. We then derive some maximal element theorems for set-valued maps in abstract convex spaces. As an application, we study the existence of solutions for a system of generalized equilibrium problems in abstract convex spaces. We also give some examples to illustrate our results.