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

Praveen Agarwal (), Mohamed Jleli and Bessem Samet
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Praveen Agarwal: Anand International College of Engineering, Department of Mathematics
Mohamed Jleli: King Saud University, Department of Mathematics, College of Sciences
Bessem Samet: King Saud University, Department of Mathematics, College of Sciences

Chapter Chapter 3 in Fixed Point Theory in Metric Spaces, 2018, pp 45-66 from Springer

Abstract: 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 equationsQuadratic integral equation is discussed. The main references of this chapter are the papers [24, 26].

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-2913-5_3

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DOI: 10.1007/978-981-13-2913-5_3

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