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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 ${A_{1}, A_{2}, \dots, A_{n + 1}}$ is a family of compact convexly connected sets in general position in $𝐑^{n}$ , then for each proper subset $I$ of ${1, 2, \dots, n + 1}$ the set of hyperplanes separating $\cup {A_{i} : i \in I}$ and $\cup {A_{j} : j \in \bar{I}}$ 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.

m-families and Common Transversals

Mircea Balaj — 1996

Publications de l'Institut Mathématique

Generalizations of the Fan-Browder fixed point theorem and minimax inequalities

Mircea Balaj; Sorin Muresan — 2005

Archivum Mathematicum

In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.

$(n + 1)$ -families of sets in general position.

Balaj, Mircea — 1996

Beiträge zur Algebra und Geometrie

An intersection theorem for set-valued mappings

Ravi P. Agarwal; Mircea Balaj; Donal 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 $x \in X$ 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.