A best proximity point theorem for generalized Mizoguchi- Takahashi contractions
DOI:
https://doi.org/10.14419/gjma.v2i2.1623الملخص
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.
المراجع
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.
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