This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces.We use Fan-KKM lemma and concept of η-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalit...

The aim of this article is obtain a Krasnoselskĭı cone compression theorem for multimaps in the class S-KKM.

We show that Fan’s 1952 lemma on labelled triangulations of the n-sphere with n + 1 labels is equivalent to the Borsuk–Ulam theorem. Moreover, unlike other Borsuk–Ulam equivalents, we show that this lemma directly implies Sperner’s Lemma, so this proof may be regarded as a combinatorial version of the fact that the Borsuk–Ulam theorem implies the Brouwer fixed-point theorem, or that the Lustern...

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game.