On the sum of simultaneously proximinal sets

Longfa SUN, Yuqi SUN, Wen ZHANG, Zheming ZHENG
2021 Hacettepe Journal of Mathematics and Statistics  
In this paper, we show that the sum of a compact convex subset and a simultaneously τ -strongly proximinal convex subset (resp. simultaneously approximatively τ -compact convex subset) of a Banach space X is simultaneously τ -strongly proximinal (resp. simultaneously approximatively τ -compact ), and the sum of a weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where τ is the norm or the
more » ... s the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented. Mathematics Subject Classification (2020). 41A65, 46B20
doi:10.15672/hujms.696407 fatcat:jlofstkjfbbgrjrjpbl2yob2hu