Pacific Journal of Mathematics

Korovkin approximations in $L_{p}$-spaces.

W. Kitto and D. E. Wulbert

Article information

Source
Pacific J. Math., Volume 63, Number 1 (1976), 153-167.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102867574

Mathematical Reviews number (MathSciNet)
MR0417658

Zentralblatt MATH identifier
0329.41018

Subjects
Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Citation

Kitto, W.; Wulbert, D. E. Korovkin approximations in $L_{p}$-spaces. Pacific J. Math. 63 (1976), no. 1, 153--167. https://projecteuclid.org/euclid.pjm/1102867574


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References

  • [1] E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, Berlin, 1971.
  • [2] P. M. Anselone, Abstract Riemann integrals, monotone approximations,and gen- eralizations of Korovkin1s theorem, Tagung uber Numerische Methoden derApproxima- tionstheorie, ISNM 15, Birkhauser, Basel, 1971.
  • [3] H. Berens and G. G. Lorentz, Korovkin sets in Banach functionspaces, Proc. Symp. on Approx. Theory, Austin, 1973, Academic Press, 1973.
  • [4] H. Berens and G. G. Lorentz, Sequences of contractionsof ^-spaces, J. of Func- tional Analysis, 15 (1974), 155-165.
  • [5] S. J. Bernau and H. E. Lacey, The range of a contractive projection on an Lv-space, Pacific J. Math., 53 (1974), 21-41.
  • [6] R. A. DeVore, The approximationof continuous functions by positive linear opera- tors, Lecture Notes in Math. 293, Springer-Verlag, Berlin, 1972.
  • [7] V. K. Dzjadyk, Approximationof functions by positive linear operators and singular integrals (Russian), Math., 56 (N.S), 70 (112), 1966, 508-517.
  • [8] C. Franchetti, Disuguaglianza e teoremi del tipo di Korovkin sugli operatori positivi in C[0,1], Boll. Delia Unione Math. Italiana, 2 (1969), 641-647. 9# fConvergenza di operatori in sottospazi dello spazio C(Q),Boll. Delia Unione Mat. Italiana, 3 (1970), 668-672.
  • [10] L. Gillman and M. Jerison, Rings of ContinuousFunctions,D. Van Nostrand, Princeton, 1960.
  • [11] R. L. James, The extension and convergence of positive operators, J. Approx. Theory, 7 (1973), 186-197.
  • [12] P. D. Korovkin, On convergence of linear positive operators in the space of con- tinuous functions, Dokl. Akad. Nauk. SSR (N.S), 90 (1953),961-969.
  • [13] M. A. Krasnosilskii and E. A. Lifsic, The principleof convergence of sequences of linear positive operators, Studia Math., 31 (1968), 455-468 (Russian).
  • [14] G. G. Lorentz, Korovkin sets, Lecture Notes, Regional Conference on Approximation Theory, Riverside, June, 1972.
  • [15] R. M. Minkova, The convergence of the derivativesof linear operators (Russian), C. R. Acad. Bulgare Sci., 23 (1970), 627-629.
  • [16] R. Nakamoto and M. Nakamura, On the theorems of Korovkin II, Proc. Japan. Acad., 41 (1965),433-435.
  • [17] Yu. A. Saskin, Systems Korovkin in the space of continuous functions,IZV 26 (1962), 495-512.
  • [18] Yu. A. Saskin, The Milman Choquet boundary and approximationtheorey, Functional Analysis AppL, 1 (1967),170-171.
  • [19] E. Schefold, Uber die punktweise konvergene von operatoren in C(X), preprint, 1972.
  • [20] H. Walk, Approximationdurch folgen linearerpositiveroperatoren, Arch. d. Math., 20 (1969), 398-404.
  • [21] M. Wolff, Uber Korovkin-satze in lokalkonvexen vektorverbanden, Math. Ann., to appear, 1973.
  • [22] D. E. Wulbert, Convergence of operators and Korovkins theorem, J.Approximation Theory, 1 (1968), 381-390.
  • [23] D. E. Wulbert, Contractive Korovkin approximations,J. Functional Analysis, 19 (1975), 205-215.
  • [24] A. V. Zaric'ka, Approximationof functionsby linear positive operators in the Lp-metric, Dopovidi Adak. Nauk Ukain, (1967), 14-17. (Russian and English summaries.)