Bulletin of the Belgian Mathematical Society - Simon Stevin

Some results on Best Proximity Points for Cyclic Mappings

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

https://projecteuclid.org/euclid.bbms/1378314516

Digital Object Identifier
doi:10.36045/bbms/1378314516

Mathematical Reviews number (MathSciNet)
MR3129059

Zentralblatt MATH identifier
1278.54043

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