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Published in:
Banach Contraction Principle and Applications Read chapter Read first chapter

2018 | OriginalPaper | Chapter

4. Cyclic Contractions: An Improvement Result

Authors : Praveen Agarwal, Mohamed Jleli, Bessem Samet

Published in: Fixed Point Theory in Metric Spaces

Publisher: Springer Singapore

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Abstract

In this chapter, we give an improvement fixed point result for cyclic contractions by weakening the closure assumption that is usually supposed in the literature. As applications, we discuss the existence of solutions to certain systems of functional equations. The main reference of this chapter is the paper [4].

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previous chapter The Class of -Contractions and Related Fixed Point Theorems
next chapter The Class of JS-Contractions in Branciari Metric Spaces
Literature
1.
Agarwal, R.P., Alghamdi, M.A., Shahzad, N.: Fixed point theory for cyclic generalized contractions in partial metric spaces. Fixed Point Theory Appl. 40 (2012)
2.
Berinde, V., Petric, M.A.: Fixed point theorems for cyclic non-self single-valued almost contractions. Carpathian J. Math. 31, 289–296 (2015)
3.
Du, W.S., Karapinar, E.: A note on Caristi-type cyclic maps: related results and applications. Fixed Point Theory Appl. 2013, 344 (2013)MathSciNetCrossRef
4.
Jleli, M., Samet, B.: An improvement result concerning fixed point theory for cyclic contractions. Carpathian J. Math. 32(3), 331–339 (2016)
5.
Karapinar, E.: Best proximity points of cyclic mappings. Appl. Math. Lett. 335, 79–92 (2007)
6.
Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4, 79–89 (2003)
7.
Mongkolkeha, C., Kumam, P.: Best proximity point theorems for generalized cyclic contractions in ordered metric spaces. J. Optim. Theory Appl. 155, 215–226 (2012)MathSciNetCrossRef
8.
Pacurar, M., Rus, I.A.: Fixed point theory for cyclic \(\varphi \)-contractions. Nonlinear Anal. 72, 1181–1187 (2010)
9.
Petric, M.A.: Some results concerning cyclical contractive mappings. General Math. 18, 213–226 (2010)
10.
Petruşel, G.: Cyclic representations and periodic points. Studia Univ. Babes-Bolyai Math. 50, 107–112 (2005)
11.
Radenović, S.: A note on fixed point theory for cyclic \(\varphi \)-contractions. Fixed Point Theory Appl. 2015, 189 (2015)
12.
Rus, I.A.: Cyclic representations and fixed points. Ann. T. Popoviciu, Seminar Funct. Eq. Approx. Convexity 3, 171–178 (2005)
Metadata
Title
Cyclic Contractions: An Improvement Result
Authors
Praveen Agarwal
Mohamed Jleli
Bessem Samet
Copyright Year
2018
Publisher
Springer Singapore
Book
Fixed Point Theory in Metric Spaces

Print ISBN: 978-981-13-2912-8

Electronic ISBN: 978-981-13-2913-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-981-13-2913-5_4

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