JP Journal of Fixed Point Theory and Applications

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GENERALIZED CONTRACTIONS IN METRIC SPACES FOR SIMULATION FUNCTION ENDOWED WITH A GRAPH

Authors

  • Nisha Kumari
  • Manoj Kumar

Keywords:

metric space, connected graph, fixed point, graphic contraction, almost contraction, generalized contraction, simulation function

DOI:

https://doi.org/10.17654/0973422822001

Abstract

This paper presents some new fixed point results for graphic contractions and Ciric-Reich-Rus $G$-contractions with the aid of simulation function endowed with a graph by generalizing the results proved by Cristian and Gabriela [4]. The case of almost contractions with respect to simulation function has also been considered.

Received: March 27, 2022
Accepted: April 25, 2022

References

H. Argoubi, B. Samet and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl. 8 (2015), 1082-1094.

V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9 (2004), 43-53.

V. Berinde, Some remarks on a fixed point theorem for Ciric-type almost contractions, Carpathian J. Math. 25(2) (2009), 157-162.

C. Cristian and P. Gabriela, Generalized contractions in metric spaces endowed with a graph, Fixed Point Theory Appl. 2012 (2012), 1-9. Article Number: 161.

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J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (2008), 1359-1373.

F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29 (2015), 1189-1194.

M. Pacurar, Iterative Methods for Fixed Point Approximations, Risoprint, Cluj-Napoca, 2010.

I. A. Rus, A. Petrusel and G. Petrusel, Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.

I. A. Rus, Picard operators and applications, Sci. Math. Jpn. 58 (2003), 191-219.

Published

2022-05-18

Issue

Section

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