Advances in nonlinear analysis via the concept of measure of noncompactness. (2017)

• Record Type: Book
• Further Information: Note: Józef Banaś, Mohamed Jleli, Mohammad Mursaleen, Bessem Samet, Calogero Vetro, editors.
• Editors: Banas, Jozef, 1950-; Jleli, Mohamed; Mursaleen, M; Samet, Bessem; Vetro, Calogero
• Contents: Preface; Contents; Editors and Contributors; 1 Measures of Noncompactness in the Space of Continuous and Bounded Functions Defined on the Real Half-Axis; 1.1 Introduction; 1.2 Notation, Definitions, and Auxiliary Facts; 1.3 Measures of Noncompactness in the Space BC (mathbbR+); 1.4 Measures of Noncompactness in the Space of Continuous Tempered Functions; 1.5 Existence of Solutions of a Quadratic Hammerstein Integral Equation in the Class of Functions Vanishing at Infinity. 1.6 Existence of Solutions of a Neutral Differential Equation with Deviating Argument in the Space of Continuous Tempered Functions1.7 Solvability of a Functional Integral Equation of Fractional Order in the Class of Functions Having Limits at Infinity; 1.8 Attractivity and Asymptotic Stability of Solutions of Functional Integral Equations; References; 2 Measures of Noncompactness and Their Applications; 2.1 Introduction; 2.2 Standard Measures of Noncompactness; 2.2.1 The Kuratowski Measure of Noncompactness; 2.2.2 The Hausdorff Measure of Noncompactness. 2.2.3 The Istrǎtescu Measure of Noncompactness2.2.4 Inner Hausdorff Measure of Noncompactness; 2.3 Measures of Noncompactness in Some Spaces; 2.3.1 Hausdorff Measure of Noncompactness in the Space C([a, b]; mathbbR); 2.3.2 Hausdorff Measure of Noncompactness in the Space Lp([a, b]; mathbbR); 2.3.3 Hausdorff Measure of Noncompactness in Banach Spaces with Schauder Bases; 2.3.4 Inner Measure of Noncompactness in Paranormed Spaces; 2.4 Constructing Measures of Noncompactness; 2.4.1 Measure of Noncompactness in C([a, b]; mathbbR); 2.4.2 Some Measures of Noncompactness in BC(mathbbR+; mathbbR). 2.6.1 An Existence Result for a Class of Nonlinear Integral Equations of Fractional Orders2.6.2 Solvability of an Implicit Fractional Integral Equation; 2.6.3 q-Integral Equations of Fractional Orders; References; 3 On Some Results Using Measures of Noncompactness; 3.1 Introduction; 3.2 Notation and Preliminaries; 3.3 The Kuratowski Measure of Noncompactness; 3.4 The Hausdorff Measure of Noncompactness; 3.5 The Istrǎţesku Measure of Noncompactness; 3.6 The Axiomatic Approach of Banaś and Goebel; 3.7 Operators; 3.8 An Equivalence Problem; 3.9 Fredholm and Semi-Fredholm Operators.
• Publisher Details: Singapore : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 515/.7248; 510; Nonlinear theories; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Nonlinear theories; Mathematics; Functional Analysis; Mathematical Modeling and Industrial Mathematics; Integral Equations; Ordinary Differential Equations; Dynamical Systems and Ergodic Theory; Operator Theory; Electronic books
• Languages: English
• ISBNs: 9789811037221; 9811037221
• Related ISBNs: 9789811037214; 9811037213
• Notes: Note: Includes bibliographical references at the end of each chapters and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed May 3, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.