A best proximity point theorem for generalized Mizoguchi- Takahashi contractions

Authors

  • Pushpendra Semwal H.N.B.Garhwal University, Srinagar Garhwal District Pauri Garhwal Uttarakhand India
  • R. Dimri H.N.B.Garhwal University, Srinagar Garhwal District Pauri Garhwal Uttarakhand India

DOI:

https://doi.org/10.14419/gjma.v2i2.1623

Published

15-04-2014

Abstract

The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for generalized Mizoguchi- Takahashi contractions. Our paper provides an extension of a result due to Gordji and Ramezani [3].

 

Keywords: Fixed point, best proximity point, P-property, Mizoguchi- Takahashi contractions.

References

A. Amini-Harandi, and D. O'Regan , "Fixed point theorem for set-valued contraction type maps in metric spaces", Fixed Point Theory and Appl, Vol.7, 2010, (2010), Article ID 390183.

A. A. Eldred, P. Veeraman, " Existence and convergence of best proximity points", J.Math.Anal. Appl, Vol.323, (2006), pp.1001-1006.

M. E.Gordji, M. Ramezani , "A generalization of Mizoguchi and Takahashi's theorem for single-valued mappings in partially ordered metric spacesr", Nonlinear Anal, Vol.74, (2011), pp.4544-4549.

N. Mizoguchi and W. Takahashi, "Fixed point theorems for multivalued mappings on a complete metric space", J.Math. Anal. Appl., Vol.141, (1989), pp.177-188.

S.B. Nadler, "Multivalued contraction mappings", Pacific j.Math, Vol.30, (1969), pp.475-488.

V. Sankar Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Analysis, vol.74 (2011), 4804-4808.

How to Cite

Semwal, P., & Dimri, R. (2014). A best proximity point theorem for generalized Mizoguchi- Takahashi contractions. Global Journal of Mathematical Analysis, 2(2), 44-49. https://doi.org/10.14419/gjma.v2i2.1623

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