Best Proximity Points for K- Proximal Contraction

Sharma, Ajay; Thakur, Balwant Singh

Research Article

Best Proximity Points for K- Proximal Contraction

Ajay Sharma¹
Balwant Singh Thakur¹*

Pt. Ravishankar Shukla University

* Corresponding author

Abstract

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

How to Cite

A. Sharma, B. S. Thakur, Best Proximity Points for K- Proximal Contraction, Int. J. Anal. Appl. 6 (2014), 82–88.

BibTeX

@article{Sharma2014,
  author  = {Sharma, Ajay and Thakur, Balwant Singh},
  title   = {Best Proximity Points for K- Proximal Contraction},
  journal = {Int. J. Anal. Appl.},
  volume  = {6},
  year    = {2014},
  pages   = {82--88},
  doi     = {}
}

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.