International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Generalized Symmetric Rational Contraction Principle in Metric Space

    , ,

Author Affiliations

  • 1Department of Mathematics, Govt. Science and Commerce College, Benazeer Bhopal, INDIA
  • 2Department of Mathematics, Govt. Science and Commerce College, Benazeer Bhopal, INDIA
  • 3Advance Material Process Research Institute, AMPRI-CSIR Bhopal, INDIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (6), Pages 1-6, July,12 (2013)

Abstract

Our aim of this paper is to introduced the concept of week symmetric rational contraction principle in metric space and prove some fixed point theorems in metric spaces. Our results are generalization and extended some previous known results. 2000 AMS Subject Classification. 54A40, 54E50, 54D35.

References

  1. Boyd D.W. and Wong J. S. W., On nonlinear contractions, Proceedings of the American Mathematical Society, 20(2), 458–464, (1969)
  2. Suzuki T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the AmericanMathematical Society, 136(5), 1861–1869 (2008)
  3. Khan M.S., Swaleh M. and Sessa S., Fixed point theorems by altering distances between the points, Bulletin of the AustralianMathematical Society, 30(1), 1–9 (1984)
  4. Ya. I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces,” in New Results in OperatorTheory and Its Applications, I. Gohberg and Y. Lyubich, Eds., vol. 98 of Operator Theory: Advances and Applications, 7–22,Birkh¨auser, Basel, Switzerland, (1997)
  5. Babu G.V.R., Lalitha B. and Sandhya M. L., Common fixed point theorems involving two generalized altering distancefunctions in four variables, Proceedings of the Jangjeon Mathematical Society, 10(1), 83–93 (2007)
  6. Naidu S.V.R., Some fixed point theorems in metric spaces by altering distances, Czechoslovak Mathematical Journal, 53(1),205–212 (2003)
  7. Sastry K.P.R. and Babu G.V.R., Some fixed point theorems by altering distances between the points, Indian Journal of Pureand Applied Mathematics, 30(6), 641–647 (1999)
  8. Sastry K.P.R., Naidu S.V.R., Babu G.V.R. and Naidu G.A., Generalization of common fixed point theorems for weaklycommuting map by altering distances, Tamkang Journal of Mathematics, 31(3), 243–250 (2000)
  9. Choudhury B.S. and Dutta P. N., A unified fixed point result in metric spaces involving a two variable function, Filomat, 14,43–48 (2000)
  10. Choudhury B.S., A common unique fixed point result inmetric spaces involving generalised altering distances, MathematicalCommunications, 10( 2), 105–110 (2005)
  11. Choudhury B.S. and Upadhyay A., On unique common fixed point for a sequence of multi-valued mappings on metricspaces, Bulletin of Pure & Applied Sciences. Section E, 19(2), 529–533 (2000)
  12. Choudhury B.S. and Dutta P.N., Common fixed points for fuzzy mappings using generalized altering distances, SoochowJournal of Mathematics, 31(1), 71–81 (2005)
  13. Choudhury B.S. and Das K., A new contraction principle in Menger Spaces, Acta Mathematica Sinica, 24(8), 1379–1386(2008)
  14. Rhoades B.E., Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods & Applications, 47(4),2683–2693 (2001)