The nonlinear superposition operator acting on Bergman spaces
The nonzero solutions and multiple solutions for a class of bilinear variational inequalities.
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
The perturbed generalized proximal point algorithm
The Perturbed Generalized Tikhonov's Algorithm
We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.
The perturbed Tikhonov's algorithm and some of its applications
The product formula.
A useful property of the Brouwerdegree relates the degree of a composition of maps to the degree of each map. This property, which can be generalized for the Leray Schauder degree and in some cases for the A-proper maps is called the Product Formula. In a previous paper we developed a generalized degree theory for a class of mappings, this class contains the class of A-proper mappings and compact mappings. In this paper we prove a generalization of the Product Formula when one factor is of the Identity+Compact...
The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
The Schauder fixed point theorem
The Schauder-Tychonoff Fixed Point Theorem and Applications
The search for fixed points under perturbations
The Secant Method and Fixed Points of Nonlinear Operators.
The semilinear Feng and FMV spectra.
The sets of fixed points of families of affine continuous mappings
The shrinking projection method for common solutions of generalized mixed equilibrium problems and fixed point problems for strictly pseudocontractive mappings.
The shrinking projection method for solving variational inequality problems and fixed point problems in Banach spaces.
The solvability of non-linear integral equations
The stationary exterior 3 D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces.
The Study of two Evolutionary random Nonlinear Problems
The super fixed point property for asymptotically nonexpansive mappings
We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.