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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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

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

First available in Project Euclid: 4 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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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