• Corpus ID: 119164514

Fixed point theorems for Meir-Keeler type contractions in metric spaces

  title={Fixed point theorems for Meir-Keeler type contractions in metric spaces},
  author={Mortaza Abtahi},
  journal={arXiv: General Topology},
  • M. Abtahi
  • Published 5 April 2016
  • Mathematics
  • arXiv: General Topology
We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic contraction of Meir-Keeler type, are Cauchy sequences. As an application, new and simple proofs for several known results on the existence of a fixed point for continuous and asymptotically regular self-maps of complete metric spaces satisfying a contractive… 
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