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

2018 | OriginalPaper | Chapter

3. The Class of \((\alpha ,\psi )\)-Contractions and Related Fixed Point Theorems

Authors : Praveen Agarwal, Mohamed Jleli, Bessem Samet

Published in: Fixed Point Theory in Metric Spaces

Publisher: Springer Singapore

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Abstract

The class of \((\alpha ,\psi )\)-contractions was introduced by Samet et al. [26]. In this chapter, we prove three fixed point theorems for this class of mappings. The presented results are extensions of those obtained in [26]. Moreover, we show that the class of \((\alpha ,\psi )\)-contractions includes as special cases several types of contraction-type mappings, whose fixed points can be obtained by means of Picard iteration. As an application, the existence and uniqueness of solutions to a certain class of quadratic integral equations is discussed. The main references of this chapter are the papers [24, 26].

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previous chapter On Ran–Reurings Fixed Point Theorem
next chapter Cyclic Contractions: An Improvement Result
Literature
1.
Argyros, I.K.: Quadratic equations and applications to Chandrasekhars and related equations. Bull. Aust. Math. Soc. 32, 275–292 (1985)MathSciNetCrossRef
2.
Argyros, I.K.: On a class of quadratic integral equations with perturbations. Funct. Approx. 20, 51–63 (1992)MathSciNetMATH
3.
Berinde, V.: Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, 43–53 (2004)MathSciNetMATH
4.
Berinde, V.: Iterative Approximation of Fixed Points. Lecture Notes in Mathematics. Springer, Berlin (2007)
5.
Chatterjee, S.K.: Fixed point theorems. Comptes Rendus Acad. Bulg. Sci. 25, 727–730 (1972)
6.
7.
Dass, B.K., Gupta, S.: An extension of Banach contraction principle through rational expressions. Indian J. Pure Appl. Math. 6, 1455–1458 (1975)MathSciNetMATH
8.
9.
Edelstein, M.: An extension of Banach’s contraction principle. Proc. Am. Math. Soc. 12, 7–10 (1961)MathSciNetMATH
10.
Hardy, G.E., Rogers, T.D.: A generalization of a fixed point theorem of Reich. Can. Math. Bull. 16, 201–206 (1973)MathSciNetCrossRef
11.
Jachymski, J.: The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136(4), 1359–1373 (2008)MathSciNetCrossRef
12.
13.
14.
Karapinar, E.: Discussion on contractions on generalized metric spaces. Abstr. Appl. Anal. 2014, Article ID 962784, 7 (2014)
15.
Karapinar, E., Samet, B.: Generalized \(\alpha \)-\(\psi \) contractive type mappings and related fixed point theorems with applications. Abstr. Appl. Anal. 2012, Article ID 793486, 17 (2014)
16.
Karapinar, E., Shahi, P., Tas, P.: Generalized \(\alpha \)-\(\psi \)-contractive type mappings of integral type and related fixed point theorems. J. Inequal. Appl. 2014, 16 (2014)
17.
Kirk, W.A., Srinivasan, P.S., Veeramany, P.: Fixed poits for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4(1), 79–89 (2003)MathSciNet
18.
Miandaragh, M.A., Postolache, M., Rezapour, S.H.: Some approximate fixed point results for generalized \(\alpha \)-contractive mappings. Univ. Politeh. Buchar. Ser. A 75(2), 3–10 (2013)MathSciNetMATH
19.
Nieto, J.J., Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22(3), 223–239 (2005)MathSciNetCrossRef
20.
Păcurar, M., Rus, I.A.: Fixed point theory for cyclic \(\phi \)-contractions. Nonlinear Anal. 72, 1181–1187 (2010)MathSciNetCrossRef
21.
Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)MathSciNetCrossRef
22.
Rezapour, S.H., Samei, M.E.: Some fixed point results for \(\alpha \)-\(\psi \)-contractive type mappings on intruitionistic fuzzy metric spaces. J. Adv. Math. Stud. 7(1), 176–181 (2014)MathSciNetMATH
23.
Rus, I.A.: Cyclic representation and fixed points. Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 3, 171–178 (2005)
24.
Samet, B.: Fixed point for \(\alpha \)-\(\psi \) contractive mappings with an application to quadratic integral equations. Electron. J. Differ. Equ. 2014, 152 (2014)MathSciNetCrossRef
25.
Samet, B.: The class of \((\alpha ,\psi )\)-type contractions in b-metric spaces and fixed point theorems. Fixed Point Theory Appl. 2015, (2015)
26.
Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for \(\alpha \)-\(\psi \)-contractive type mappings. Nonlinear Anal. 75(4), 2154–2165 (2012)MathSciNetCrossRef
27.
Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness. Proc. Am. Math. Soc. 136, 1861–1869 (2008)MathSciNetCrossRef
28.
Suzuki, T.: Some similarity between contractions and Kannan mappings. Fixed Point Theory Appl. 2008, Article ID 649749, 1–8 (2008)
29.
Metadata
Title
The Class of -Contractions and Related Fixed Point Theorems
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_3

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