• Corpus ID: 119164514

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

@article{Abtahi2016FixedPT,
  title={Fixed point theorems for Meir-Keeler type contractions in metric spaces},
  author={Mortaza Abtahi},
  journal={arXiv: General Topology},
  year={2016}
}
  • 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… 
Common fixed point theorems of Meir-Keeler type in metric spaces
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In this paper, fixed point theorems for Ćirić-Matkowski-type contractions in $$\nu $$ν-generalized metric spaces are presented. Then, by replacing the distance function d(x, y) with function of the
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A self-map T of a ν-generalized metric space (X,d) is said to be a ´ Ciric-Matkowski contraction if d(Tx,Ty) 0, there is δ > 0 such that d(x,y) 0, results analogue to those due to P.D. Proiniv (Fixed
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  • Mathematics
    Differential and Integral Inequalities
  • 2019
Some fixed point results are given for a class of Meir–Keeler sequential contractions acting on relational metric spaces. The connections with a related statement in Turinici [MDMFPT, Paper-3-3, Pim,
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