In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

This paper presents new random fixed point theorems and random Leray–Schauder alternatives for a variety of maps (e.g., Bκ, Uκ c , KKM and PK maps). A random Kransnoselskii cone compression theorem for Uκ c maps is also given. Various random approximation theorems for the above classes are proved and as applications several random fixed point theorems are also derived.

Let S be the unit d-sphere, the set of all points of unit Euclidean distance from the origin in R . Any pair of points in S of the form x,−x is a pair of antipodes in S. Let ∆ be the d-simplex formed by the convex hull of the standard unit vectors in R. Equivalently, ∆ = {(x1, ..., xd+1) : ∑ i xi = 1, xi ≥ 0}. The following are two classical results about closed covers of these topological spaces:

Economic Models and Generalized Games 229 4.

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...

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...