Common fixed point of four maps in b-metric spaces

Common fixed point of four maps in b-metric spaces

In this paper, some common fixed point results for four mappings satisfying generalized contractive condition in a b-metric space are proved.Advantage of our work in comparison with studies done in the contextof b-metric is that, the b-metric function used in the theorems andresults are not necessarily continuous. So, our results extend and improve several comparable results obtained previously. We also presenttwo examples that show the applicability and validity of our results.

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  • [1] Abbas, M. and Nazir, T. Fixed points of T -Hardy Rogers type contraction mapping in G -metric spaces, Afrika Matematika, 2012.
  • [2] Aghajani, A. Abbas, M and Roshan, J. R. Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, to appear in Math. Slovaca.
  • [3] Akkouchi, M. Common fixed point theorems for two selfmappings of a b-metric space under an implicit relation, Hacettepe Journal of Mathematics and Statistics, Volume 40(6), 805- 810. 2011.
  • [4] Aydi, H. Bota, M. Karapınar, E. and Mitrovi´c, S. A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl, 2012: 88. 2012.
  • [5] Aydi, H. Bota, M. Karapinar, E. and Moradi, S. A common fixed point for weak ?- contractions on b-metric spaces, Fixed Point Theory, Vol. 13, No. 2, 337-346. 2012.
  • [6] Boriceanu, M. Strict fixed point theorems for multivalued operators in b-metric spaces, International Journal of Modern Mathematics, 4(3), 285-301, 2009.
  • [7] Boriceanu, M. Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. "Babes-Bolyai", Mathematica, Volume LIV, Number 3, 2009.
  • [8] Boriceanu, M. and Bota, M. and Petrusel, A. Multivalued fractals in b-metric spaces, Cent. Eur. J. Math, 8 (2), 367-377, 2010.
  • [9] Bota, M. Molnar, A. and Varga, C. On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, 12 (2), 21-28, 2011.
  • [10] Ciri´c, L.B. Generalized contraction and fixed point theorems, Publications de l´ Institut Mathe´matique, vol. 12, no. 26, pp. 19-26, 1971.
  • [11] Ciri´c, L.B. A generalization of Banach´s contraction principle, Proceedings of the American Math-ematical Society, vol. 45, pp. 267-273, 1974.
  • [12] Czerwik, S. Contraction mappings in b-metric spaces, Acta Math Inf Univ Ostraviensis.1, 5-11, 1993.
  • [13] Czerwik, S. Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46(2), 263-276, 1998.
  • [14] Czerwik, S, Dlutek, K. Singh, S. L. Round-off stability of iteration procedures for set-valued operators in b-metric Spaces. J Nature Phys Sci., 11, 87-94. 2007.
  • [15] Hardy, G.E. and Rogers, T.D. A generalization of a fixed point theorem of Reich, Canadian Math-ematical Bulletin, vol. 16, pp. 201-206, 1973.
  • [16] Hussain, N. Dori´c, D. Kadelburg, Z. and Radenovi´c, S. Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., doi:10.1186/1687-1812-2012-126, 2012.
  • [17] Hussain, N. and Shah, M.H. KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62, 1677-1684, 2011.
  • [18] Jovanovi´c, M. Kadelburg, Z. and Radenovi´c S. Common fixed point results in metric-type spaces, Fixed Point Theory Appl , Article ID 978121, 15 pages, 2010.
  • [19] Jungck, G. Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4), 771-779, 1986.
  • [20] Khamsi, M.A. Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl, Article ID 315398, 7 pages, doi:10.1155/2010/315398, 2010.
  • [21] Khamsi, M.A. Hussain, N. KKM mappings in metric type spaces, Nonlinear Anal., 73(9), 3123-3129, 2010.
  • [22] Nashine, H.K. and Kadelburg, Z. Common fixed point theorems under weakly Hardy- Rogers-type contraction conditions in ordered orbitally complete metric spaces, Racsam, doi: 10.1007/s13398-012-0106-2, 2012.
  • [23] Shah, M.H. and Hussain, N. Nonlinear contractions in partially ordered quasi b-metric spaces, Commun. Korean Math. Soc., 27, No. 1, pp. 117-128, 2012.
  • [24] Shukla, S. Radenovi´c, S. and Panteli´c, S. Some fixed point theorems for pre?si´c-Hardy-Rogers type contractions in metric spaces, Journal of Mathematics, Volume 2013, ArticleID 295093, 8 pages.
  • [25] Singh, S.L. and Prasad, B. Some coincidence theorems and stability of iterative proceders, Comput. Math. Appl., 55, 2512-2520, 2008.
  • [26] Pacurar, M. Sequences of almost contractions and fixed points in b-metric spaces, Analele Universitatii de Vest, Timisoara Seria Matematica Informatica XLVIII, 3, 125-137, 2010.
  • [27] Alaeidizaji, H. and Parvaneh, V. Coupled Fixed Point Results in Complete Partial Metric Spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2012, Article ID 670410, 12 pages.