Best proximity point theorems for cyclic quasi-contraction maps in uniformly convex Banach spaces. (English) Zbl 1452.90318
Summary: In this paper, we first give a negative answer to a question of A. Amini-Harandi [J. Glob. Optim. 56, No. 4, 1667–1674 (2013; Zbl 1291.90305)] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi [loc.cit.]for cyclic strongly quasi-contractions are true under weaker assumptions.
MSC:
| 90C48 | Programming in abstract spaces |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Citations:
Zbl 1291.90305References:
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