Naseer Shahzad, Maryam Alghamdi, and Ghada Alnemer. On Best Proximity Points of Multivalued Nonexpansive Mappings. Dynamic Systems and Applications 30 (2021) No.3, 411-424

https://doi.org/10.46719/dsa20213037

ABSTRACT.
In [2], Abkar and Gabeleh established the existence of a best proximity point for a multivalued nonexpansive nonself-mapping in a Banach space. The domain of the mapping is compact, which is a very strong condition for applications. We relax this strong condition and generalize their result using the asymptotic center method. We also prove the existence of best proximity points for multivalued upper semicontinuous and nonexpansive mappings defined on a proximinal pair in a Banach space. We illustrate some examples to support our results.

Keywords: Best proximity point, Multivalued nonexpansive mapping, Fixed point, Asymptotic radius, Asymptotic center, Proximinal parallel, Generalized contraction, WP-property, Opial condition.

 AMS (MOS) Subject Classification. 47H10, 47H09, 47H04, 54H25.