Fixed Point of Mappings in Ĝ–Dualistic Partial Metric Space Endowed with a Graph

Authors

  • Neeraj Kumar Department of Mathematics, M.D.U, Rohtak, 124001,(HR), India
  • Seema Mehra Department of Mathematics, M.D.U, Rohtak, 124001, (HR), India

Keywords:

Ĝ - Dualistic partial metric space, Ĝ -CCP, Fixed point, Graph.

Abstract

This paper aims is to find out the fixed points for two mappings in Ĝ - dualistic partial metric space with the help of graph by using Ĝ - Convergence Comparison Property (Ĝ - CCP). An application is also given to find fixed point with the help of boundary value problem.

Downloads

Download data is not yet available.

References

A. Bejenaru, A. Pitea, Fixed point and best proximity point theorems on partial metric spaces , J. Math. Anal.7 (2016) 25-44.

A. Phon-on, A. Sama-Ae*, N. Makaje,P. Riyapan, S. Busaman, Coincidence point theorems for weak graph preserving multi-valued mapping,Fixed Point Theory and Applications. 248 (1) (2014) (2014). DOI:https://doi.org/10.1186/1687-1812-2014-248.

B.K. Dass , S. Gupta, An extension of Banach contraction principle through rational expressions,Indian journal of Pure and Applied mathematics.6 (1975) 1455 - 1458.

D. W. Boyd, J.S.W. Wong, Nonlinear contractions, Proc. Amer. Math. Soc. 20 (2) (1969) 458-464.DOI:https://doi.org/10.1090/S0002-9939-1969-0239559-9.

G. Cornelissena ,M. Marcolli ,Graph reconstruction and quantum statistical mechanics,Journal of Geometry and Physics. 72 (2013) 110-117.DOI: https://doi.org/10.1016/j.geomphys.2013.03.021.

J. Jachymski, The contraction principle for mappings on a metric space with a graph,Proceddings of the american mathematical society.136 (4) (2008) 1359-1373.DOI:https://doi.org/10.1090/s0002-9939-07-09110-1.

K.F Ciesielski, On Stefan Banach and some of his results, Banach J. Math. Anal.1 (1) (2007) 1-10.DOI: https://doi.org/10.15352/bjma/1240321550.

M. Nazam, M. Arshad,M.Abbas, Some fixed point results for dualistic partial metric spaces,Applied General Topology.17 (2) (2016) 199-209.DOI: https://doi.org/10.4995/agt.2016.5920

M. Nazam,A.Mukheimer,H.Aydi,M.Arshad,R.Riaz,Fixed point results for Dualistic Contractions with an Application,Discrete Dynamics in Nature and Society.2020 (2020) 9.Article ID 6428671.DOI:https://doi.org/10.1155/2020/6428671.

M.A. Alghmadi, N.Shahzad,O.Valero, on fixed point theory in partial metric spaces, Fixed Point Theory Appl.2012 (1) (2012) 175.DOI:https://doi.org/10.1186/1687-1812-2012-175.

M.Arshad, A.Shoaib, M. Abbas, A.Azam,Fixed points of a pair of kannan type mappings on a closed ball in ordered partial metric spaces, Miskolc Math. Notes 14 (3) (2013) 769-784.DOI: https://doi.org/10.18514/mmn.2013.722.

M.Laurent ,Cuts, matrix completions and graph rigidity,Mathematical Programming. 79 (1) (1997) 255-283.DOI: https://doi.org/10.1007/bf02614320.

R.M.T. Bianchini,Su un problems di S. Reich riguardante la teoria dei punti fissi,Bollettino dellunione Mathematica Italian.5 (1972) 103-108.

S.G. Matthews,Partial metric topology,Ann. New York Acad Sci. 728 (1) (1994)183-197.DOI:https://doi.org/10.1111/j.1749-6632.1994.tb44144.x.

S.J.O’Neiil,Partial metric , valuations and domain theory.Annals of the new york academy of science.806 (1) (1996) 304-315.DOI:https://doi.org/10.1111/j.1749-6632.1996.tb49177.x.

S.Oltra, O. Valero, Banach’s fixed point theorem for partial metric spaces ,Rend.Istit.Mat.Univ.Trieste 36 (2004) 17-26.

S.Reiech, Some Remarks concerning contractions mappings canadian Mathematical Bulletin Society.13(3) (1971) 121-124.DOI:https://doi.org/10.4153/CMB-1971-024-9.

W. Shatanawi,M. Postolache,Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces,Fixed Point Theory Appl.2013 (1) (2013),Art.No. 54.DOI: https://doi.org/10.1186/1687-1812-2013-54.

W. Shatanawi,M. Postolache,Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces ,Fixed Point Theory Appl.2013 (1) (2013), Art.No. 271.DOI:https://doi.org/10.1186/1687-1812-2013-271.

Ya. I. Alber, S.Guerrre-Delabriere, Principles of weakly contractive maps in Hilbert space, New Res.Oper.Theory Appl.98 (1997) 7-22.

Graph of a fixed point of A and B

Downloads

Published

17.10.2022

How to Cite

Neeraj Kumar, & Seema Mehra. (2022). Fixed Point of Mappings in Ĝ–Dualistic Partial Metric Space Endowed with a Graph. International Journal of Intelligent Systems and Applications in Engineering, 10(1s), 363–375. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/2302

Issue

Vol. 10 No. 1s (2022)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

All papers should be submitted electronically. All submitted manuscripts must be original work that is not under submission at another journal or under consideration for publication in another form, such as a monograph or chapter of a book. Authors of submitted papers are obligated not to submit their paper for publication elsewhere until an editorial decision is rendered on their submission. Further, authors of accepted papers are prohibited from publishing the results in other publications that appear before the paper is published in the Journal unless they receive approval for doing so from the Editor-In-Chief.

IJISAE open access articles are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. This license lets the audience to give appropriate credit, provide a link to the license, and indicate if changes were made and if they remix, transform, or build upon the material, they must distribute contributions under the same license as the original.