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

Balaj, Mircea — 1996

Beiträge zur Algebra und Geometrie

Haar spaces and polynomial selections.

Balaj, Mircea; Wa̧sowicz, Szymon — 2003

Mathematica Pannonica

Fixed points and minimax inequalities.

Balaj, Mircea; Erzse, Daniel — 2004

Acta Universitatis Apulensis. Mathematics - Informatics

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.

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.

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 $S_{n}^{+}$ .

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.

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.

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