Maximal semigroups dominated by 0-1 matrices.
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances.
Mean value theorem for convex functionals
Measure of noncompactness of operators and matrices on the spaces and .
Measure of non-compactness of operators interpolated by the real method
We study the measure of non-compactness of operators between abstract real interpolation spaces. We prove an estimate of this measure, depending on the fundamental function of the space. An application to the spectral theory of linear operators is presented.
Measure of noncompactness of subsets of Lebesgue spaces
Measure of nonhyperconvexity and fixed-point theorems.
Measure of weak noncompactness under complex interpolation
Logarithmic convexity of a measure of weak noncompactness for bounded linear operators under Calderón’s complex interpolation is proved. This is a quantitative version for weakly noncompact operators of the following: if T: A₀ → B₀ or T: A₁ → B₁ is weakly compact, then so is for all 0 < θ < 1, where and are interpolation spaces with respect to the pairs (A₀,A₁) and (B₀,B₁). Some formulae for this measure and relations to other quantities measuring weak noncompactness are established.
Measures of noncircularity and fixed points of contractive multifunctions.
Measures of noncompactness and normal structure in Banach spaces
Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
Measures of noncompactness in Banach sequence spaces
Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets
In this paper we prove a collection of new fixed point theorems for operators of the form on an unbounded closed convex subset of a Hausdorff topological vector space . We also introduce the concept of demi--compact operator and -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum of two operators, where is -sequentially continuous and -compact while is -sequentially continuous (and -condensing, -nonexpansive...
Measures of non-compactness in Orlicz modular spaces.
In this paper we show that the ball-measure of non-compactness of a norm bounded subset of an Orlicz modular space L-Psi is equal to the limit of its n-widths. We also obtain several inequalities between the measures of non-compactness and the limit of the n-widths for modular bounded subsets of L-Psi which do not have Delta-2-condition. Minimum conditions on Psi to have such results are specified and an example of such a function Psi is provided.
Measures of noncompactness in the study of solutions of nonlinear differential and integral equations
The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.
Measures of non-strict-singularity of operators
Measures of weak noncompactness in Banach sequence spaces.
Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Method of semidiscretization in time for quasilinear integrodifferential equations.
Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions.
Méthode de descente sur un fermé non convexe