Existence of best proximity points for controlled proximal contraction. (English) Zbl 1347.54093
Summary: In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our results improve and generalize some existing results on the topic in the literature, in particular, the results of T.-C. Lim [J. Math. Anal. Appl. 110, 436–441 (1985; Zbl 0593.47056)] and of A. Abkar and M. Gabeleh [Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 107, No. 2, 319–325 (2013; Zbl 1287.54036)].
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54C60 | Set-valued maps in general topology |
| 54E40 | Special maps on metric spaces |
References:
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