New Version For Hardy And Rogers type Mapping in Dislocated Metric Space

Authors and Affiliations

  • sumati kumari panda Asst.Professor K L University vaddeswaram India.
  • V Vasantha Kumar
  • I Rambhadra sarma

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Abstract

In this paper we establish a common fixed point theorem for two pairs of weakly Compatible maps in dislocated metric( -metric) spaces. The purpose of this note is to prove the -metric versions for weakly compatible maps of new version for Hardy and Rogers[7] theorem which ultimately implies existence (and uniqueness in some cases) of  common fixed points for weakly compatible maps that satisfy conditions analogous to those of Banach, Kannan and Chatterjea [5].

Author Biography

  • sumati kumari panda, Asst.Professor K L University vaddeswaram India.

    Ass.Professor,

    Department of mathematics,

    K L University.

    Two gold Medals From Indian Government

    Eight Awards From Indian Government

References

[1] P. Hitzler, Generalized Metrics and Topology in Logic Programming Semantics, Ph.D.Thesis, National University of Ireland,(University College, Cork), 2001.

[2] Gerald jungck, Proceedings of the American Mathematical Society, vol. 103, no.3July 1988,977-983

[3] P Sumati kumari, On dislocated quasi metrics, Jour. of Adv. Stu. in Top,Vol. 3, no. 2,2012, 66 – 74.

[4] G. Jungck, Common fixed points for noncontinuous nonself mappings on a nonmetricspace, Far East J. Math. Sci. 4(2)(1996), 199–212.

[5] B.E.Rhoades, A comparison of various definitions of contractive mappings,Trans of the Amer.Math.Society vol 226(1977) 257-290.

View more references (2)

[6] S.Sedghi and N.Shobe, Common fixed point theorems for four mappings in complete Metric space, Bulletin of the Iranian Mathematical Society Vol. 33 No. 2 (2007), pp 37-47

[7] G E Hardy and T D Rogers, A Generalization of a fixed point theorem of Reich,canad. Math. Bull. 16, 201-206,(1973).


How to Cite

panda, sumati kumari, Kumar, V. V., & sarma, I. R. (2012). New Version For Hardy And Rogers type Mapping in Dislocated Metric Space. International Journal of Basic and Applied Sciences, 1(4), 609-617. https://doi.org/10.14419/ijbas.v1i4.431