Search results for " measure of noncompactness"

showing 3 items of 3 documents

A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

2019

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

Class (set theory)Mathematics (miscellaneous)Fixed point problemSettore MAT/05 - Analisi MatematicaGeneralizationApplied MathematicsMeasure (physics)Applied mathematicsFixed pointIntegral equationFixed point measure of noncompactness simulation function integral equation.MathematicsResults in Mathematics
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Examples of proper k-ball contractive retractions in F-normed spaces

2007

Abstract Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r ( X ) of radius r is properly contained in X . The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a ( 1 + e ) -ball contractive retraction of B r ( X ) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X .

Discrete mathematicsPure mathematicsApplied Mathematicsρ-Near retractionk-Ball contractionRegular F-normed ideal spaceRetractionHausdorff measure of noncompactnessHausdorff measureBall (mathematics)Hausdorff measure of noncompactneF-spaceAnalysisNormed vector spaceMathematicsJournal of Mathematical Analysis and Applications
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Compactness in Groups of Group-Valued Mappings

2022

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Fréchet–Šmulian and Ascoli–Arzelà compactness criteria found in the literature.

equimeasurabilitySettore MAT/05 - Analisi MatematicaGeneral Mathematicsuniform quasiboundednessComputer Science (miscellaneous)convergence (and local convergence) in measuremeasure of noncompactnessgroupgroup; pseudonorm; convergence (and local convergence) in measure; measure of noncompactness; equimeasurability; uniform quasiboundednesspseudonormEngineering (miscellaneous)Mathematics
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