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


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


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


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.


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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:

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:

G. Cornelissena ,M. Marcolli ,Graph reconstruction and quantum statistical mechanics,Journal of Geometry and Physics. 72 (2013) 110-117.DOI:

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:

K.F Ciesielski, On Stefan Banach and some of his results, Banach J. Math. Anal.1 (1) (2007) 1-10.DOI:

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

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:

M.A. Alghmadi, N.Shahzad,O.Valero, on fixed point theory in partial metric spaces, Fixed Point Theory Appl.2012 (1) (2012) 175.DOI:

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:

M.Laurent ,Cuts, matrix completions and graph rigidity,Mathematical Programming. 79 (1) (1997) 255-283.DOI:

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:

S.J.O’Neiil,Partial metric , valuations and domain theory.Annals of the new york academy of science.806 (1) (1996) 304-315.DOI:

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:

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:

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:

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




How to Cite

Neeraj Kumar and Seema Mehra, “Fixed Point of Mappings in Ĝ–Dualistic Partial Metric Space Endowed with a Graph”, Int J Intell Syst Appl Eng, vol. 10, no. 1s, pp. 363–375, Oct. 2022.