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august 2013 Some results on Best Proximity Points for Cyclic Mappings
H. K. Pathak, N. Shahzad
Bull. Belg. Math. Soc. Simon Stevin 20(3): 559-572 (august 2013). DOI: 10.36045/bbms/1378314516


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.


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H. K. Pathak. N. Shahzad. "Some results on Best Proximity Points for Cyclic Mappings." Bull. Belg. Math. Soc. Simon Stevin 20 (3) 559 - 572, august 2013.


Published: august 2013
First available in Project Euclid: 4 September 2013

zbMATH: 1278.54043
MathSciNet: MR3129059
Digital Object Identifier: 10.36045/bbms/1378314516

Primary: 47H09 , 47H10 , 54H25

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

Rights: Copyright © 2013 The Belgian Mathematical Society


Vol.20 • No. 3 • august 2013
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