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Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets

Józef Banaś, Afif Ben Amar (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove a collection of new fixed point theorems for operators of the form $T + S$ on an unbounded closed convex subset of a Hausdorff topological vector space $(E, Γ)$ . We also introduce the concept of demi- $τ$ -compact operator and $τ$ -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum $T + S$ of two operators, where $T$ is $τ$ -sequentially continuous and $τ$ -compact while $S$ is $τ$ -sequentially continuous (and $Φ_{τ}$ -condensing, $Φ_{τ}$ -nonexpansive...

Measures of non-compactness in Orlicz modular spaces.

A. G. Aksoy, J.-B. Baillon (1993)

Collectanea Mathematica

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

Józef Banaś (2012)

Open Mathematics

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 and Non-strict-cosingularity

Snežana Živković (2002)

Matematički Vesnik

Measures of non-strict-singularity of operators

V. R. Rakočević (1983)

Matematički Vesnik

Measures of weak noncompactness in Banach sequence spaces.

Banas, Jozef, Martinón, Antonio (1995)

Portugaliae Mathematica

Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines

Ahmed Zeriahi (1987)

Annales de l'institut Fourier

Soit $K$ un compact polynomialement convexe de $C^{n}$ et $V_{K}$ son “potentiel logarithmique extrémal” dans $C^{n}$ . Supposons que $K$ est régulier (i.e. $V_{K}$ continue) et soit $f$ une fonction holomorphe sur un voisinage de $K$ . On construit alors une suite ${P_{ℓ}}_{ℓ \geq 1}$ de polynôme de $n$ variables complexes avec deg $(P_{)} \leq ℓ$ pour $ℓ \geq 1$ , telle que l’erreur d’approximation $\max_{z \in K} | f (z) - P_{ℓ} (z) |$ soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de $f$ par rapport à $K$ et du degré de convergence $ℓ$ . Ce résultat est ensuite utilisé pour étendre...

Meir-Keeler contractions of integral type are still Meir-Keeler contractions.

Suzuki, Tomonari (2007)

International Journal of Mathematics and Mathematical Sciences

Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights.

A. Böttcher, Y. Karlovich (1998)

Manuscripta mathematica

Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study

A. Pimenov, T.C. Kelly, A. Korobeinikov, M.J.A. O’Callaghan, A.V. Pokrovskii, D. Rachinskii (2012)

Mathematical Modelling of Natural Phenomena

Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour...