"10.1007/s00209-011-0915-6" . "[3A60EC954C37]" . "On the approximate fixed point property in abstract spaces" . "Lin, P-K" . . . "On the approximate fixed point property in abstract spaces" . "RIV/00216208:11320/12:10127319!RIV13-AV0-11320___" . . "000306342700035" . "271" . . "On the approximate fixed point property in abstract spaces"@en . "http://dx.doi.org/10.1007/s00209-011-0915-6" . "Barroso, C. S." . . . . . . "RIV/00216208:11320/12:10127319" . "P(IAA100190901), Z(MSM0021620839)" . . "1"^^ . "Mathematische Zeitschrift" . "156353" . . . "15"^^ . . . "3"^^ . "Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X *. In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X *, and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces."@en . . "On the approximate fixed point property in abstract spaces"@en . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . . "Frechet-Urysohn space; l_1 sequence; Metrizable locally convex space; Weak approximate fixed point property"@en . "3-4" . "Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X *. In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X *, and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces." . "11320" . "0025-5874" . . "Kalenda, Ond\u0159ej" . .