%0 Journal Article %T Two Continuity Concepts in Approximation Theory %A Asnaashari, Hossein %J Journal of Mathematics and Computer Science %D 2012 %V 4 %N 1 %@ ISSN 2008-949X %F Asnaashari2012 %X In this note, we study various continuity criteria for the set-valued metric projection onto a set \(V\). Also we introduce some simpler and more general radial continuity criteria. %9 journal article %R 10.22436/jmcs.04.01.05 %U http://dx.doi.org/10.22436/jmcs.04.01.05 %P 32--36 %0 Journal Article %T Suns, moons, and quasi-polyhedra %A D. Amir %A F. Deutsch %J J. Approximation Theory %D 1972 %V 6 %F Amir1972 %0 Journal Article %T Čebyšev sets in Hilbert space %A E. Asplund %J Trans. Amer. Math. Soc. %D 1969 %V 144 %F Asplund1969 %0 Journal Article %T Zur Stetigkeit von mengenwertigen metrischen Projektionen %A J. Blatter %J In: Quasi-Nullsummenspiele und dominierte Gleichgewichtspunkte in Bimatrix-Spielen %D 1967 %V 1967 %F Blatter1967 %0 Journal Article %T Continuity of the set-valued metric projection %A J. Blatter %A P. D. Morris %A D. Wulbert %J Math. Ann. %D 1968 %V 178 %F Blatter1968 %0 Journal Article %T Weiteste Punkte und nächste Punkte %A J. Blatter %J Rev. Roumaine Math. Pures Appl. %D 1969 %V 14 %F Blatter1969 %0 Journal Article %T Charakterisierung bester Approximationen in normierten Vektorrumen %A B. Brosowski %A R. Wegmann %J J. Approximation Theory %D 1970 %V 3 %F Brosowski1970 %0 Book %T On the lower semi-continuity of the set-valued metric projection %A B. Brosowski %A R. Wegmann %D 1973 %I J. Approximation Theory %C Vol. 8, 84--100 %F Brosowski1973 %0 Journal Article %T Über eine Fixpunkteigenschaft der metrischen Projektion %A B. Brosowski %J Computing %D 1970 %V 5 %F Brosowski1970 %0 Book %T On some geometric properties of suns %A B. Brosowski %A F. Deutsch %D 1974 %I J. Approximation Theory %C Vol. 10, 245--267 %F Brosowski1974 %0 Journal Article %T Best n-dimensional approximation to sets of functions %A A. L. Brown %J Proc. London Math. Soc. %D 1964 %V 14 %F Brown1964 %0 Book %T Linear operators part I: general theory %A N. Dunford %A J. T. Schwartz %D 1958 %I Interscience publishers %C New York %F Dunford1958 %0 Book %T Reelle Funktionen: Erster Teil: Punktfunktionen %A H. Hahn %D 1948 %I Chelsea Publishing Company %C Chelsea %F Hahn1948 %0 Journal Article %T Remarks on nearest points in normed linear spaces %A V. Klee %J In: Proc. Colloq. Convexity (Copenhagen) %D 1965 %V 1965 %F Klee1965 %0 Journal Article %T Some new continuity concepts for metric projections %A B. Brosowski %A F. Deutsch %J Bull. Amer. Math. Soc. %D 1972 %V 78 %F Brosowski1972 %0 Journal Article %T Extension of compact operators %A J. Lindenstrauss %J American Mathematical Soc. %D 1964 %V 1964 %F Lindenstrauss1964 %0 Journal Article %T Metric projections onto subspaces of finite codimension %A P. D. Morris %J Duke Math. J. %D 1968 %V 35 %F Morris1968 %0 Journal Article %T Continuity of metric projection and some geometric properties of the unit sphere in a Banach space %A E. V. Oshman %J Doklady Akademii Nauk %D 1969 %V 185 %F Oshman1969 %0 Book %T On set-valued metric projections %A I. Singer %D 1972 %I In: Linear Operators and Approximation/Lineare Operatoren und Approximation %C 217--233 %F Singer1972 %0 Journal Article %T Approximation properties of sets in normed linear spaces %A S. B. Steckin %J Rev. Roumaine Math. Pures Appl. %D 1963 %V 8 %F Steckin1963 %0 Journal Article %T Approximatively convex sets in Banach spaces %A L. P. Vlasov %J Dokl. Akad. Nauk SSSR %D 1965 %V 6 %F Vlasov1965 %0 Journal Article %T Chebyshev sets and approximatively convex sets %A L. P. Vlasov %J Matematicheskie Zametki (Russian) %D 1967 %V 2 %F Vlasov1967