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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 thedoi:10.15672/hujms.696407 fatcat:jlofstkjfbbgrjrjpbl2yob2hu