Feng-Liu type approach to best proximity point results for multivalued mappings. (English) Zbl 1431.54039
In [J. Math. Anal. Appl. 317, 103–112 (2006; Zbl 1094.47049)], Y.-Q. Feng and S.-Y. Liu generalized the Banach contraction principle and Caristi’s fixed point theorem to the case of multi-valued mappings by using a contractive condition that does not involve the Pompeiu-Hausdorff metric, see, for example, the paper [V. Berinde and M. Păcurar, Creat. Math. Inf. 22, No. 2, 143–150 (2013; Zbl 1313.47114)].
In the paper under review, the authors use the Feng-Liu approach to study the existence of best proximity points of multi-valued mappings.
In the paper under review, the authors use the Feng-Liu approach to study the existence of best proximity points of multi-valued mappings.
Reviewer: Vasile Berinde (Baia Mare)
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54C60 | Set-valued maps in general topology |
| 54E40 | Special maps on metric spaces |
| 54E50 | Complete metric spaces |
Keywords:
metric space; Banach contraction principle; Caristi’s fixed point theorem; Pompeiu-Hausdorff metric; best proximity point; multi-valued mappingReferences:
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