Best Proximity Points for K- Proximal Contraction

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Ajay Sharma, Balwant Singh Thakur, Best Proximity Points for K- Proximal Contraction, Int. J. Anal. Appl., 6 (1) (2014), 82-88.

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Ajay Sharma, Balwant Singh Thakur

Abstract

In this paper, we define K- proximal contraction and prove best proximity point theorem for this contraction. We also provide an illustrative example.

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References

  1. Ya. I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications, Oper. Theory Adv. Appl., 98 (1997), 7-22.
  2. S. Almezel, Q.H. Ansari, and M.A. Khamsi(eds.), Topics in Fixed Point Theory, Springer, 2014.
  3. S. Sadiq Basha, Best Proximity Points: Optimal Solutions, J. Optim. Theory Appl. 151 (2011) no.1, 210-216.
  4. S. Sadiq Basha,Best proximity point theorems: resolution of an important non-linear programming problem, Optim. Lett. 7 (2013), no.6, 1167-1177.
  5. S. Sadiq Basha and N. Shahzad, Best proximity point theorems for generalized proximal contractions, Fixed Point Theory Appl., 2012(2012), Article ID 42.
  6. S. Sadiq Basha and P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103(2000), 119-129.
  7. S.K. Chatterjee, Fixed point theorems, Comptes. Rend. Acad. Bulgaria Sci. 25(1972), 727- 730.
  8. Binayak S. Choudhury, Unique fixed point theorem for weakly C-contractive mappings, Kathmandu university journal of science,engineering and technology, 5(2009), no.I, 6-13.
  9. Vasile I. Istratescu Fixed Point Theory: An Introduction (Mathematics and Its Applications), Springer, 1981.
  10. M. A. Khamsi and W.A. Kirk, An introduction to metric spaces and fixed point theory, Pure and Applied Mathematics (New York). Wiley-Interscience, New York, 2001.
  11. M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984) no.1 , 1-9.
  12. W.A. Kirk, and B. Sims(eds.), Handbook of metric fixed point theory, Kluwer Academic Publishers, Dordrecht, 2001.
  13. D. Mihet, Altering distances in probabilistic Menger spaces, Nonlinear Anal. 71(2009), 2734- 2738.
  14. S.V.R. Naidu, Some fixed point theorems in Metric spaces by altering distances, Czech. Math. J. 53 (2003), no.1, 205-212.
  15. B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001) 2683- 2693.
  16. V. Sankar Raj, A best proximity theorem for weakly contractive non-self mappings, Nonlinear Anal. 74 (2011), 4804-4808.
  17. K.P.R. Sastry and G.V.R. Babu, Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math. 30 (1999),no.6, 641-647.
  18. D. R Smart, Fixed point theorems, Cambridge University Press, London, 1974. Cambridge Tracts in Mathematics, No. 66.