Averaging operators and set-valued maps

MSC 2010: 54C35, 54C60.

Porosity and Variational Principles

We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

Dense Continuity and Selections of Set-Valued Mappings

∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Selections, Paracompactness and Compactness

2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.

String Measure Applied to String Self-Organizing Maps and Networks of Evolutionary Processors

* Supported by projects CCG08-UAM TIC-4425-2009 and TEC2007-68065-C03-02

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

Rétractes Absolus de Voisinage Algébriques

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.