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2002 | 22 | 2 | 243-260
Tytuł artykułu

Best approximations, fixed points and parametric projections

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EN
Abstrakty
EN
If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].
Twórcy
  • University of Perugia, Department of Mathematics and Computer Science, Via Vanvitelli, 1 - 06123 Perugia, Italy
Bibliografia
  • [1] B. Brosowsky and F.N. Deutsch, Radial continuity of valued metric projections, J. Approx. Theory 11 (1974), 236-253.
  • [2] B. Brosowsky, F.N. Deutsch and G. Nurnberger, Parametric approximation, J. Approx. Theory 29 (1980), 261-277.
  • [3] T. Cardinali and F. Papalini, Sull'esistenza di punti fissi per multifunzioni a grafo debolmente chiuso, Riv. Mat. Univ. Parma (4) 17 (1991), 59-67.
  • [4] T. Cardinali and F. Papalini, Fixed point theorems for multifunctions in topological vector spaces, J. Math. Anal. Appl. 186 (3) (1994), 769-777.
  • [5] F. Deutsch, Theory of best approximation in normed linear spaces, Mimeographed notes, 1972.
  • [6] K. Fan, Extensions of two fixed point theorems of F.E. Browder, Math. Z. 112 (1969), 234-240.
  • [7] N.I. Glebov, On a generalization of the Kakutani fixed point theorem, Soviet Math. Dokl. 10 (1969), 446-448.
  • [8] P. Govindarajulu and D.V. Pai, On properties of sets related to f-projections, J. Math. Anal. Appl. 73 (1980), 457-465.
  • [9] G. Köthe, Topological vector spaces (I), Springer-Verlag, Berlin, Heidelberg, New York 1969.
  • [10] T.C. Lin, A note on a theorem of Ky Fan, Canad. Math. Bull. 22 (1979), 513-515.
  • [11] S. Mabizela, Upper semicontinuity of parametric projection, Set Valued Analysis 4 (1996), 315-325.
  • [12] T.D. Narang, On f-best approximation in topological spaces, Archivum Mathematicum, Brno 21 (4) (1985), 229-234.
  • [13] T.D. Narang, A note of f-best approximation in reflexive Banach space, Matem. Bech. 37 (1985), 411-413.
  • [14] E.V. Oshman, On the continuity of metric projection in Banach space, Math. USSR Sb. 9 (1969), 171-182.
  • [15] S. Reich, Approximate selections, best approximations, fixed points and invariant sets, J. Math. Anal. Appl. 62 (1978), 104-113.
  • [16] V.M. Seghal and S.P. Singh, A theorem on the minimization of a condensing multifunction and fixed points, J. Math. Anal. Appl. 107 (1985), 96-102.
  • [17] I. Singer, The theory of best approximation and functional analysis, Regional Conference Series in Applied Math., Philadelphia 1974.
  • [18] C. Waters, Ph. D. thesis, Univ. of Wyoming 1984.
  • [19] E. Zeidler, Nonlinear Functional Analysis and its Applications II/A, Springer-Verlag 1990.
  • [20] E. Zeidler, Variational methods and optimization III, Springer-Verlag 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1041
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