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Coincidence points and maximal elements of multifunctions on convex spaces

Sehie Park — 1995

Commentationes Mathematicae Universitatis Carolinae

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

Sehie Park — 1996

Commentationes Mathematicae Universitatis Carolinae

Let X be a uniformly convex Banach space, D X , f : D X a nonexpansive map, and K a closed bounded subset such that co ¯ K D . If (1) f | K is weakly inward and K is star-shaped or (2) f | K satisfies the Leray-Schauder boundary condition, then f has a fixed point in co ¯ K . 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.

On zeros and fixed points of multifunctions with non-compact convex domains

Sehie ParkJong Sook Bae — 1993

Commentationes Mathematicae Universitatis Carolinae

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

Lai-Jiu LinChing-Jung KoSehie Park — 1998

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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