Fixed Points for the \(G\)-Contraction on \(E\)-\(b\)-Metric Spaces with a Graph

Authors

  • Rahul Hooda Department of Mathematics, Maharshi Dayanand University, Rohtak, India https://orcid.org/0000-0003-1519-9385
  • Mamta Kamra Department of Mathematics, Indira Gandhi University, Meerpur, Rewari, India
  • Archana Malik Department of Mathematics, Maharshi Dayanand University, Rohtak, India

DOI:

https://doi.org/10.26713/cma.v12i4.1538

Keywords:

Fixed points, E-b-metric space, Graph, Banach G-contraction

Abstract

In this paper, we study fixed points for the \(G\)-contraction on \(E\)-\(b\)-Metric spaces endowed with a graph. The work in this paper should be seen as a generalization of [7].

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References

I. A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Functional Analysis 30 (1989), 26 – 37.

C. Cevik and I. Altun, Vector metric spaces and some properties, Topological Methods in Nonlinear Analysis 34(2009), 375 – 382, URL: https://apcz.umk.pl/czasopisma/index.php/TMNA/article/view/TMNA.2009.048.

S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostrviensis 1 (1993), 5 – 11, URL: https://dml.cz/bitstream/handle/10338.dmlcz/120469/ActaOstrav_01-1993-1_2.pdf.

I. R. Petre, Fixed point theorems in E-b-metric spaces, Journal of Nonlinear Sciences and Applications 7 (2014), 264 – 271, DOI: 10.22436/jnsa.007.04.04.

C. Cevik, On continuity of functions between vector metric spaces, Journal of Function Spaces (2014), 1 – 6, DOI: 10.1155/2014/753969.

M. Kamra, S. Kumar and K. Sarita, Some fixed point theorems for self mappings on Vector bmetric spaces, Global Journal of Pure and Applied Mathematics 14, 11 (2018), 1489 – 1507, URL: https://www.ripublication.com/gjpam18/gjpamv14n11_06.pdf.

J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society 136 (2008), 1359 – 1373, DOI: 10.1090/S0002-9939-07-09110-1.

R. Espinola and W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology and its Applications 153 (2006), 1046 – 1055, DOI: 10.1016/j.topol.2005.03.001.

R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society 60 (1968), 71 – 76.

M. Samreen, T. Kamran and N. Shahzad, Some fixed point theorems in b-metric space endowed with graph, Abstract and Applied Analysis 2013 (2013), Article ID 967132, 9 pages, DOI: 10.1155/2013/967132.

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Published

13-12-2021
CITATION

How to Cite

Hooda, R., Kamra, M. ., & Malik, A. . (2021). Fixed Points for the \(G\)-Contraction on \(E\)-\(b\)-Metric Spaces with a Graph. Communications in Mathematics and Applications, 12(4), 803–813. https://doi.org/10.26713/cma.v12i4.1538

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Section

Research Article