# 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} }

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…

## 5 Citations

Common fixed point theorems of Meir-Keeler type in metric spaces

- Mathematics
- 2017

This paper is a continuation of the recent work [M. Abtahi, Fixed point theorems for Meir-Keeler type contractions in metric spaces, Fixed Point Theory, 17(2016), No. 2, 225-236]. After establishing…

Fixed points of Ćirić-Matkowski-type contractions in $$\nu $$ν-generalized metric spaces

- Mathematics
- 2017

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…

IN GENERALIZED METRIC SPACES

- Mathematics
- 2015

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…

Meir–Keeler Sequential Contractions and Applications

- MathematicsDifferential 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,…

Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces

- MathematicsApplied General Topology
- 2018

New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized…

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