Articles

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

  • Vesna COJBASIC RAJIC ,
  • Stojan RADENOVIC ,
  • Sunny CHAUHAN
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  • Faculty of Economics, University of Belgrade, Kamenicka 6, 11000 Beograd, Serbia; Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120 Beograd, Serbia; R. H. Government Postgraduate College, Kashipur-244 713 (U.S. Nagar),Uttarakhand, India

Received date: 2011-12-29

  Revised date: 2012-12-14

  Online published: 2014-07-20

Supported by

First and second author are thankful to the Ministry of Education, Science and Technological Development of Serbia.

Abstract

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (φψ )-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

Cite this article

Vesna COJBASIC RAJIC , Stojan RADENOVIC , Sunny CHAUHAN . COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1345 -1356 . DOI: 10.1016/S0252-9602(14)60088-6

References

[1] Abbas M, Jungck J. Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J Math Anal Appl, 2008, 341: 416–420

[2] Abbas M, Ali Khan M. Common fixed point theorem of two mappings satisfying a generalized weak con-tractive condition. Int J Math Math Sci, 2009, 2009: Article ID 131068

[3] Ahmad A G B, Fadail Z M, ´Cojbaˇsi´c Raji´c V, Radenovi´c S. Nonlinear contractions in 0-complete partial metric spaces. Abstract Appl Anal, 2012, 2012: Article ID 451239

[4] Aydi H, Abbas M, Vetro C. Partial Hausdorff metric and Nadler´s fixed point theorem on partial metric spaces. Topology Appl, 2012, 159(14): 3234–3243

[5] Aydi H, Vetro C, Shatanawi W, Kumam P. Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces. Fixed Point Theory Appl, 2012, 2012: 124

[6] Abdeljawad T. Fixed points for generalized weakly contractive mappings in partial metric spaces. Math Comput Model, 2011, 54: 2923–2927

[7] Abdeljawad T, Karapinar E, Tas K. A generalized contraction principle with control functions on partial metric spaces. Comput Math Appl, 2012, 6: 716–719

[8] Abdeljawad T, Karapinar E, Tas K. Existence and uniqueness of a common fixed point on partial metric spaces. Appl Math Lett, 2011, 24: 1900–1904

[9] Alber Ya I, Guerre-Delabriere S. Principle of weakly contractive maps in Hilbert spaces//Gohberg I, Lyubich Yu, ed. New Results in Operator Theory, Advances and Appl. Basel: Birkhauser Verlag, 1997, 98: 7–22

[10] Altun I, Erduran A. Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl, 2011, 2011: Article ID 508730

[35] Berinde V, Vetro F. Common fixed point of mappings satisfying implicit contractive conditions. Fixed Point Theory Appl, 2012, 2012: 105

[12] ´Ciri´c Lj B, Samet B, Aydi H, Vetro C. Common fixed points of generalized contractions on partial metric spaces and applications. Appl Math Comput, 2011, 218: 2398–2406

[13] Di Bari C, Milojevi´c M, Radenovi´c S, Vetro P. Common fixed points for self-mappings on partial metric spaces. Fixed Point Theory Appl, 2012, 2012: 140

[14] Di Bari C, Vetro P. Common fixed points for  -contractions on partial metric spaces. To appear in Hacet J Math Stat

[15] Di Bari C, Vetro P. Fixed points for weak  -contractions on partial metric spaces. Int J of Engineering, Contemporary Mathematics and Sciences, 2011, 1: 5–13

[16] Di Bari C, Kadelburg Z, Nashine H K, Radenovi´c S. Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces. Fixed Point Theory Appl, 2012, 2012: 113

[17] Dutta P N, Choudhury B S. A generalization of contraction principle in metric spaces. Fixed Point Therory Appl, 2008, 2008: Article ID 406368

[18] –Duki´c D, Kadelburg Z, Radenovi´c S. Fixed points of Geraghty-type mappings in various generalized metric spaces. Abstract Appl Anal, 2011, 2011: Article ID 561245

[19] –Dori´c D. Common fixed point for generalized ( ψ, φ)-weak contractions. Appl Math Lett, 2009, 22: 1896–1900

[20] Huang X, Zhu C, Wen X. Fixed point theorems for expanding mappings in partial metric spaces. An St Univ Ovidius Constanta, 2012, 20(1): 213–224

[21] Ili´c D, Pavlovi´c V, Rakoˇcevi´c V. Some new extensions of Banach´s contractions principle in partial metric
spaces. Appl Math Lett, 2011, 24: 1326–1330

[22] Ili´c D, Pavlovi´c V, Rakoˇcevi´c V. Extensions of Zamfirescu theorem to partial metric spaces. Math Comput
Model, 2012, 55: 801–809

[23] Kadelburg Z, Nashine H K, Radenovi´c S. Fixed point results under various contractive conditions in partial metric spaces. RASCAM, 2013, 107(2): 241–256

[24] Karapinar E, Erhan I M. Fixed point theorems for operators on partial metric spaces. Appl Math Lett, 2011, 24: 1894–1899

[25] Khan M S, Swaleh M, Sessa S. Fixed point theorems by altering distances between the points. Bull Aust Math Soc, 1984, 30: 1–9

[26] Matthews S G. Partial Metric Topology. Research Report 212. Dept of Computer Science, University of Warwick, 1992

[27] Matthews S G. Partial metric topology//Proc 8th Summer Conference on General Topology and Applica-tions. Ann New York Acad Sci, 1994, 728: 183–197

[28] Nashine H K, Kadelburg Z, Radenovi´c S. Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces. Math Comput Model, 2013, 57(9/10): 2355–2365

[29] Nashine H K, Kadelburg Z, Radenovi´c S, Kim J K. Fixed point theorems under Hardy-Rogers contractive conditions on 0-complete ordered partial metric spaces. Fixed Point Theory Appl, 2012, 2012: 180

[30] O’Neill S J. Partial metrics, valuations and domain theory//Proc 11th Summer Conference on General Topology and Applications. Ann New York Acad Sci, 1996, 806: 304–315

[31] O’Neill S J. Two topologies are better than one. Tech report, University of Warwick, Conventry, UK,
http://www.dcs.warwick.ac.uk/reports/283.html.1995

[32] Oltra S, Valero O. Banach’s fixed point theorem for partial metric spaces. Rend Istit Math Univ Trieste, 2004, 36: 17–26

[33] Paesano D, Vetro P. Suzuki’s type characterizations of completeness for partial metric spacers and fixed points for partially ordered metric spaces. Topology Appl, 2012, 159: 911–920

[34] Radenovi´c S, Kadelburg Z, Jandrli´c D, Jandrli´c A. Some results on weakly contractive maps. Bull Iran Math Soc, 2012, 38(3): 625–645

[35] Rhoades B E. Some theorems on weakly contractive maps. Nonlinear Anal, 2001, 47: 2683–2693

[36] Romaguera S. Fixed point theorems for generalized contractions on partial metric spaces. Topology Appl, 2011, 159: 194–199

[37] Romaguera S. Kirk A. Type characterization of completeness for partial spaces. Fixed Point Theory Appl, 2010, 2010: Article ID 493298

[38] Samet B, Rajovi´c M, Lazovi´c R, Stoiljkovi´c R. Common fixed point results for nonlinear contractions in ordered partial metric spaces. Fixed Point Theory Appl, 2011, 2011: 71

[39] Vetro F, Radenovi´c S. Nonlinear  -quasi-contractions of ´Ciri´c-type in partial metric spaces. Appl Math Comput, 2012, 219(4): 1594–1600

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