Implicit Contractions on a Set Equipped with Two Metrics

  • Praveen AgarwalEmail author
  • Mohamed Jleli
  • Bessem Samet


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 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].


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

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