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.

Approximation of Lipschitz Mappings

2000 Mathematics Subject Classification: 46B03

Selections, Paracompactness and Compactness

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

Spline Subdivision Schemes for Compact Sets. A Survey

Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel

Fragmentability of the Dual of a Banach Space with Smooth Bump

We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.

Speculating About Mountains

∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria.

Uniform Convergence of the Newton Method for Aubin Continuous Maps

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

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model

2000 Mathematics Subject Classification: Primary: 62M10, 62J02, 62F12, 62M05, 62P05, 62P10; secondary: 60G46, 60F15.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

Averaging operators and set-valued maps

MSC 2010: 54C35, 54C60.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.