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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

4. Space of Functions with Growths Tempered by a Modulus of Continuity

Authors : I. J. Cabrera, J. Harjani, B. López, K. B. Sadarangani

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

Publisher: Springer Singapore

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Abstract

The principal aim of this chapter is to consider the function space consisting of functions defined on a compact metric space with growths tempered by a given modulus of continuity and its connection with the measures of noncompactness. The chapter is inspired in the papers [1, 2].

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previous chapter On Some Results Using Measures of Noncompactness
next chapter Measure of Noncompactness in Functional Fractional Calculus
Literature
1.
Banaś, J., Nalepa, R.: On the space of functions with growths tempered by a modulus of continuity and its applications. J. Function Spaces 820437, 13 (2013)
2.
Banaś, J., Nalepa, R.: On a measure of noncompactness in the space of functions with tempered increments. J. Math. Anal. Appl. 435, 1634–1651 (2016)
3.
Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lect. Notes Pure Appl. Math. Dekker, New York (1980)
4.
Darbo, G.: Punti uniti in transformazioni a condominio non compatto. Rend. Semin. Mat. Univ. Padova. 24, 84–92 (1955)MathSciNetMATH
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6.
Zhao, Y., Sun, S., Han, Z., Li, Q.: Positive solutions to boundary value problems of nonlinear fractional differential equations. Abstr. Appl. Anal. 390543, 16 (2011)
7.
Caballero, J., Harjani, J., Sadarangani, K.: On existence and uniqueness of positive solutions to a class of fractional boundary problems. Bound. Value Probl. 2011(95), 9 (2011)
8.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies. Elsevier Science B.V, Amsterdam (2006)
9.
Yu, Y., Jiang, D.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Northeast Normal University (2009)
10.
Aghajani, A., Banaś, J., Sabzali, N.: Some generalizations of Darbo fixed point theorem and applications. Bull. Belg. Math. Soc. 20, 345–358 (2013)
11.
Aghajani, A., Allahyari, R., Mursaleen, M.: A generalization of Darbo’s theorem with application to the solvability of systems of integral equations. J. Comp. Appl. Math. 260, 68–77 (2014)MathSciNetCrossRefMATH
12.
Dhage, B.C., Dhage, S.B., Pathak, H.K.: A generalization of Darbo’s fixed point theorem and local attractivity of generalized nonlinear functional integral equations. Differ. Equ. Appl. 1, 57–77 (2015)MathSciNetMATH
Metadata
Title
Space of Functions with Growths Tempered by a Modulus of Continuity
Authors
I. J. Cabrera
J. Harjani
B. López
K. B. Sadarangani
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_4

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