"401" . . "Optimal approximate fixed point results in locally convex spaces"@en . "Let C be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps f:C -> (C) over bar. First, we prove that, if f (C) is totally bounded, then it has an approximate fixed point net. Next, it is shown that, if C is bounded but not totally bounded, then there is a uniformly continuous map f:C -> C without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping of a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, we construct an affine sequentially continuous map from a compact convex set into itself without fixed points." . . "000314739000001" . "Let C be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps f:C -> (C) over bar. First, we prove that, if f (C) is totally bounded, then it has an approximate fixed point net. Next, it is shown that, if C is bounded but not totally bounded, then there is a uniformly continuous map f:C -> C without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping of a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, we construct an affine sequentially continuous map from a compact convex set into itself without fixed points."@en . . . "Kalenda, Ond\u0159ej" . . . . "1" . "Barroso, C. S." . "RIV/00216208:11320/13:10173727" . "Optimal approximate fixed point results in locally convex spaces" . . "11320" . "http://dx.doi.org/10.1016/j.jmaa.2012.10.026" . "0022-247X" . "Reboucas, M. P." . "3"^^ . "RIV/00216208:11320/13:10173727!RIV14-GA0-11320___" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "Optimal approximate fixed point results in locally convex spaces"@en . . . "10.1016/j.jmaa.2012.10.026" . "P(GAP201/12/0290)" . "[C1F123FB070A]" . . "Uniformly continuous map; Sequentially continuous map; Totally bounded set; Approximate fixed point sequence; Approximate fixed point net"@en . "1"^^ . . "8"^^ . "Journal of Mathematical Analysis and Applications" . . "94284" . . . "Optimal approximate fixed point results in locally convex spaces" . .