Fixed points, intersection theorems, variational inequalities, and equilibrium theorems.
Extensions of best approximation and coincidence theorems.
On fixed points of set-valued directional contractions.
Generalizations of the Nash equilibrium theorem in the KKM theory.
Remarks on weakly KKM maps in abstract convex spaces.
New versions of the Fan-Browder fixed point theorem and existence of economic equilibria.
Remarks on extensions of the Himmelberg fixed point theorem.
Generalized variational inequalities of the Hartman-Stampacchia-Browder type.
Saddle point theorems on generalized convex spaces.
Characterizations of metric completeness
Coincidence points and maximal elements of multifunctions on convex spaces
Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.
On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces
Let be a uniformly convex Banach space, , a nonexpansive map, and a closed bounded subset such that . If (1) is weakly inward and is star-shaped or (2) satisfies the Leray-Schauder boundary condition, then has a fixed point in . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.
A general vector-valued variational inequality and its fuzzy extension.
The Idzik type quasivariational inequalities and noncompact optimization problems
On zeros and fixed points of multifunctions with non-compact convex domains
Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave functions on convex spaces, we obtain extended versions of the existence theorem of H. Ben-El-Mechaiekh [2] on zeros for multifunctions with non-compact domains, the coincidence theorem of S.H. Kum [5] for upper hemicontinuous multifunctions, and the Ky Fan type fixed point theorems due to E. Tarafdar [13].
Coincidence theorems for set-valued maps with g-kkm property on generalized convex space
In this paper, a set-valued mapping with G-KKM property is defined and a generalization of minimax theorem for set-valued maps with G-KKM property on generalized convex space is established. As a consequence of this results we verify the coincidence theorem for set-valued maps with G-KKM property on G-convex space. Finally, we apply our results to the best approximation problem and fixed point problem.
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