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Measures of Noncompactness in the Space of Continuous and Bounded Functions Defined on the Real Half-Axis Read chapter Read first chapter

2017 | OriginalPaper | Chapter

2. Measures of Noncompactness and Their Applications

Authors : Mohammad Mursaleen, Syed M. H. Rizvi, Bessem Samet

Published in: Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

Publisher: Springer Singapore

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Abstract

In this chapter, we present a survey of theory and applications of measures of noncompactness. The standard measures of noncompactness are discussed and their properties are compared. Some results concerning standard measures of noncompactness in different spaces including \(C([a,b];\mathbb {R})\), \(L^p([a,b];\mathbb {R})\), Banach spaces with Schauder bases, and paranormed spaces are presented. Moreover, we study different classes of operators, for which we establish fixed point results via an arbitrary measure of noncompactness in the sense of Banaś and Goebel. Finally, we present some applications of the measure of noncompactness concept to functional equations including nonlinear integral equations of fractional orders, implicit fractional integral equations and q-integral equations of fractional orders.

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previous chapter Measures of Noncompactness in the Space of Continuous and Bounded Functions Defined on the Real Half-Axis
next chapter On Some Results Using Measures of Noncompactness
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Metadata
Title
Measures of Noncompactness and Their Applications
Authors
Mohammad Mursaleen
Syed M. H. Rizvi
Bessem Samet
Copyright Year
2017
Publisher
Springer Singapore
Book
Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

Print ISBN: 978-981-10-3721-4

Electronic ISBN: 978-981-10-3722-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-981-10-3722-1_2

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