Bulletin of the Belgian Mathematical Society - Simon Stevin

Some results on Best Proximity Points for Cyclic Mappings

H. K. Pathak and N. Shahzad

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Abstract

In this paper we consider a cyclic $\varphi_A$-contraction mapping defined on a partially ordered orbitally complete metric space and prove some fixed point and best proximity point theorems. We also discuss some relationship between points of coincidence and common best proximal points. It is shown that, under certain condition, a point of coincidence, a common best proximal point and a common fixed point coincide.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 3 (2013), 559-572.

Dates
First available in Project Euclid: 4 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1378314516

Digital Object Identifier
doi:10.36045/bbms/1378314516

Mathematical Reviews number (MathSciNet)
MR3129059

Zentralblatt MATH identifier
1278.54043

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Keywords
Point of Coincidence Fixed point Best proximity point Cyclic contraction mapping Cyclic $\varphi_A$-contraction mapping Property UC

Citation

Pathak, H. K.; Shahzad, N. Some results on Best Proximity Points for Cyclic Mappings. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 3, 559--572. doi:10.36045/bbms/1378314516. https://projecteuclid.org/euclid.bbms/1378314516


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