Ionel Rovenţa

Fan’s inequality in geodesic spaces

Abstract Fan’s minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained.

Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature

The Schauder fixed point theorem is extended to the context of metric spaces with global nonpositive curvature. Some applications are included.

A note on Schur-concave functions

In this paper we consider a class of Schur-concave functions with some measure properties. The isoperimetric inequality and Brunn-Minkowsky’s inequality for such kind of functions are presented. Applications in geometric programming and optimization theory are also derived.MSC:26B25, 26B15, 52A40.

Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities

We consider a new class of nonlinearities for which a nonlocal parabolic equation with Neumann boundary conditions has finite time blow-up solutions. Our approach is inspired by previous work done by Jazar and Kiwan (2008) and El Soufi et al. (2007).

Approximation of the controls for the linear beam equation

This article deals with the approximation of the boundary controls of a 1-D linear equation modeling the transversal vibrations of a hinged beam using a finite-difference space semi-discrete scheme. Due to the high frequency numerical spurious oscillations, the semi-discrete model is not uniformly controllable with respect to the mesh size and the convergence of the approximate controls corresponding to initial data in the finite energy space cannot be guaranteed. In this paper we analyze how do the initial data to be controlled and their discretization affect the result of the approximation process. We prove that the convergence of the scheme is ensured if the continuous initial data are sufficiently regular or if the highest frequencies of their discretization have been filtered out. In both cases, the minimal weighted

Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method

L^2

Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem

L2-norm discrete controls are shown to be convergent to the corresponding continuous one when the mesh size tends to zero.

An approach of majorization in spaces with a curved geometry

We study a generalized equilibrium problem by using a nonsymmetric extension of Ky Fan’s inequality. As an application, we present a fixed point type algorithm inspired by a model from Tada and Takahashi (2007).