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Advances in nonlinear analysis via the concept of measure of noncompactness

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful...

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Other Authors: Banas, Jozef, 1950-, Jleli, Mohamed,, Mursaleen, M.,, Samet, Bessem,, Vetro, Calogero,, SpringerLink (Online service)
Format: eBook
Language: English
Published: Singapore : Springer, 2017.
Physical Description: 1 online resource.
Subjects:
Nonlinear theories.
Mathematics.
Functional analysis.
Integral equations.
Dynamics.
Ergodic theory.
Operator theory.
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245 0 0 |a Advances in nonlinear analysis via the concept of measure of noncompactness /  |c Józef Banaś, Mohamed Jleli, Mohammad Mursaleen, Bessem Samet, Calogero Vetro, editors. 
264 1 |a Singapore :  |b Springer,  |c 2017. 
300 |a 1 online resource. 
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505 0 |6 880-01  |a 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. 
505 8 |a 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. 
505 8 |a 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). 
505 8 |a 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. 
500 |a Includes index. 
588 0 |a Online resource; title from PDF title page (SpringerLink, viewed May 3, 2017). 
520 |a This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book's central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus. 
504 |a Includes bibliographical references at the end of each chapters and index. 
650 0 |a Nonlinear theories. 
650 1 0 |a Mathematics. 
650 2 0 |a Functional analysis. 
650 2 4 |a Mathematical Modeling and Industrial Mathematics. 
650 2 0 |a Integral equations. 
650 2 4 |a Ordinary Differential Equations. 
650 2 0 |a Dynamics. 
650 2 0 |a Ergodic theory. 
650 2 0 |a Operator theory. 
650 6 |a Théories non linéaires. 
650 7 |a MATHEMATICS  |x Calculus.  |2 bisacsh. 
650 7 |a MATHEMATICS  |x Mathematical Analysis.  |2 bisacsh. 
650 7 |a Análisis funcional.  |2 embne. 
650 7 |a Nonlinear theories.  |2 fast. 
700 1 |a Banas, Jozef,  |d 1950-  |1 https://id.oclc.org/worldcat/entity/E39PBJbRgv6JrywvjgDx4DhWDq,  |e editor. 
700 1 |a Jleli, Mohamed,  |e editor. 
700 1 |a Mursaleen, M.,  |e editor. 
700 1 |a Samet, Bessem,  |e editor. 
700 1 |a Vetro, Calogero,  |e editor. 
710 2 |a SpringerLink (Online service) 
776 0 8 |i Print version:  |t Advances in nonlinear analysis via the concept of measure of noncompactness.  |d Singapore : Springer, 2017  |z 9811037213  |z 9789811037214  |w (OCoLC)967373871. 
880 8 |6 505-01/(S  |a 2.4.3 Measure of Noncompactness with Kernel2.5 Fixed Point Theorems Involving a Measure of Noncompactness; 2.5.1 The Class of o-Contractive Mappings and Darbo's Fixed Point Theorem; 2.5.2 A Fixed Point Theorem for (|,)-o-Contractive Mappings; 2.5.3 A Fixed Point Theorem for -o-Contractive Mappings; 2.5.4 A Fixed Point Theorem for an Implicit o-Contraction; 2.5.5 A Fixed Point Theorem for k-o-Contractive Mappings; 2.5.6 Meir--Keeler Generalization of Darbo's Theorem; 2.5.7 A Fixed Point Result in a Banach Algebra; 2.6 Some Applications of the Measure of Noncompactness Concept. 
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