Abstract
Let X be a real or complex Banach space and let F subset X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x in X , R_F(x) ne emptyset , where RF(x)={d∈F:‖d-c‖≤‖x-c‖for anyc∈F}.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} R_F (x) = \\{ d \\in F : \\Vert d-c\\Vert \\le \\Vert x-c\\Vert \\hbox { for any } c \\in F \\} . \\end{aligned}$$\\end{document}It is clear that any existence set is a contractive subset of X. The aim of this paper is to present some conditions on F and X under which the notions of exsistence set and contractive set are equivalent.
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