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Constant selections and minimax inequalities

Mircea Balaj — 2006

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.

Separation of ( n + 1 ) -families of sets in general position in 𝐑 n

Mircea Balaj — 1997

Commentationes Mathematicae Universitatis Carolinae

In this paper the main result in [1], concerning ( n + 1 ) -families of sets in general position in 𝐑 n , is generalized. Finally we prove the following theorem: If { A 1 , A 2 , , A n + 1 } is a family of compact convexly connected sets in general position in 𝐑 n , then for each proper subset I of { 1 , 2 , , n + 1 } the set of hyperplanes separating { A i : i I } and { A j : j I ¯ } is homeomorphic to S n + .

Admissible maps, intersection results, coincidence theorems

Mircea Balaj — 2001

Commentationes Mathematicae Universitatis Carolinae

We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.

An intersection theorem for set-valued mappings

Ravi P. AgarwalMircea BalajDonal O'Regan — 2013

Applications of Mathematics

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T : X X , S : Y X we prove that under suitable conditions one can find an x X which is simultaneously a fixed point for T and a common point for the family of values of S . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.

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