Implicit Contractions on a Set Equipped with Two Metrics

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 6 in Fixed Point Theory in Metric Spaces, 2018, pp 89-100 from Springer

Abstract: Abstract Several classical fixed point theorems have been unified by considering general contractions expressed via an implicit inequality, see, for examples, Turinici [15], Popa [8, 9], Berinde [2], and references therein. In this chapter, we consider a class of mappings defined on a set equipped with two metrics and satisfying an implicit contractionImplicit contraction involving two functions $$F:[0,\infty )^6\rightarrow \mathbb {R}$$ and $$\alpha : X\times X\rightarrow \mathbb {R}$$ . The existence of fixed points for this class of mappings is investigated. The main reference for this chapter is the paper [14].

Date: 2018
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DOI: 10.1007/978-981-13-2913-5_6

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