Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 20, Number 3 (2013), 559-572.
Some results on Best Proximity Points for Cyclic Mappings
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.
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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Digital Object Identifier
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]
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