A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES

doi:10.1016/S0252-9602(14)60004-7

Abstract

Abstract:

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki´s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.

Key words: Fixed and common fixed points, Suzuki fixed point theorem, partial G-metric spaces

CLC Number:

47H10

Peyman SALIMI, Pasquale VETRO. A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES[J].Acta mathematica scientia,Series B, 2014, 34(2): 274-284.

Trendmd

References

[1] Aull C E, Lowen R. Handbook of the history of general topology. Dodrecht: Kluwer, 2001

[2] Blumenthal L M. Distance geometry. London: Oxford Univ Press, 1953

[3] Hadˇzi´c O, Pap E. Fixed point theory in probabilistic metric spaces. London: Kluwer, 2001

[4] Kirk W A, Sims B. Handbook of metric fixed point theory. Kluwer, 2001

[5] 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

[6] Romaguera S. A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl, 2010, 2010: Article ID 493298, 6 pages

[7] Kirk W A. Caristi’s fixed point theorem and metric convexity. Colloq Math, 1976, 36: 81–86

[8] Mustafa Z. A new structure for generalized metric spaces with applications to fixed point theory. PhD Thesis. Australia: The University of Newcastle, 2005

[9] Mustafa Z, Sims B. A new approach to generalized metric spaces. J Nonlinear Convex Anal, 2006, 7(2): 289–297

[10] Abbas M, Nazir T, Radenovi´c S. Common fixed point of generalized weakly contractive maps in partially ordered G-metric spaces. Appl Math Comput, 2012, 218(18): 9383–9395

[11] Abbas M, Nazir T, Vetro P. Common fixed point results for three maps in G-metric spaces. Filomat, 2011, 25(4): 1–17

[12] Kadelburg Z, Nashine H K, Radenovi´c S. Common coupled fixed point results in partially ordered G-metric spaces. Bull Math Anal Appl, 2012, 4: 51–63

[13] Long W, Abbas M, Nazir T, Radenovi´c S. Common fixed point for two pairs of mappings satisfying (E.A) property in generalized metric spaces. Abstr Appl Anal, 2012, 2012: Article ID 394830, 15 pp

[14] Mustafa Z, Obiedat H. A fixed point theorem of Reich in G-metric spaces. CUBO, 2010, 12(1): 83–93

[15] Mustafa Z, Shatanawi W, Bataineh M. Existence of fixed point results in G-metric spaces. Int J Math Math Sci, 2009, 2009: Article ID 283028, 10 pages

[16] Mustafa Z, Sims B. Fixed point theorems for contractive mappings in complete G-metric spaces. Fixed Point Theory Appl, 2009, 2009: Article ID 917175, 10 pages

[17] Radenovi´c S, Panteli´c S, Salimi P, Vujakovi´c J. A note on some tripled coincidence point results in G-metric spaces. Int J Math Sci Eng Appl, 2012, 6(6): 23–38

[18] Saadati R, Vaezpour S M, Vetro P, Rhoades B E. Fixed point theorems in generalized partially ordered G-metric spaces. Math Comput Modelling, 2010, 52(5/6): 797–801

[19] Shatanawi W. Fixed point theory for contractive mappings satisfying -maps in G-metric spaces. Fixed Point Theory Appl, 2010, 2010: Article ID 181650, 9 pages

[20] Shatanawi W. Some fixed point theorems in ordered G-metric spaces and applications. Abst Appl Anal, 2011, 2011: Article ID 126205, 11 pages

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

[22] Suzuki T. A generalized Banach contraction principle that characterizes metric completeness. Proc Amer Math Soc, 2008, 136: 1861–1869

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

[24] 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

[25] Haghi R H, Rezapour Sh, Shahzad N. Some fixed point generalizations are not real generalizations. Non-linear Anal, 2011, 74: 1799–1803