On best proximity points of upper semicontinuous multivalued mappings

被引：0
作者：
AlNemer G. [1 ,2 ]
Markin J. [3 ]
Shahzad N. [1 ,4 ]
机构：
[1] Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah
[2] Department of Mathematics, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh
[3] 528 Rover Boulevard, Los Alamos, 87544, NM
[4] Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah
来源：
Fixed Point Theory and Applications | / 2015卷 / 1期
关键词：
best proximity point; fixed point; multivalued mapping; relatively u-continuous mapping; upper semicontinuous mapping;
D O I：
10.1186/s13663-015-0489-9
中图分类号：
学科分类号：
摘要：
In this paper we study the existence of best proximity points of a nonself upper semicontinuous multivalued mapping T:A→2B$T:Arightarrow2^{B}$ in a strictly convex Banach space. This multivalued mapping commutes with affine, noncyclic, and relatively u-continuous single-valued mapping f:A∪B→A∪B$f:A cup Brightarrow Acup B$. Also, we study the case when T commutes with a family of commuting, affine, noncyclic, and relatively u-continuous single-valued mappings on A∪B$Acup B$. Moreover, we present some examples to illustrate our results. © 2015, AlNemer et al.
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页码：1 / 10
页数：9
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