Approximation of continuous convex-cone-valued functions by monotone operators

João Prolla

Studia Mathematica (1992)

  • Volume: 102, Issue: 2, page 175-192
  • ISSN: 0039-3223

Abstract

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In this paper we study the approximation of continuous functions F, defined on a compact Hausdorff space S, whose values F(t), for each t in S, are convex subsets of a normed space E. Both quantitative estimates (in the Hausdorff semimetric) and Bohman-Korovkin type approximation theorems for sequences of monotone operators are obtained.

How to cite

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Prolla, João. "Approximation of continuous convex-cone-valued functions by monotone operators." Studia Mathematica 102.2 (1992): 175-192. <http://eudml.org/doc/215921>.

@article{Prolla1992,
abstract = {In this paper we study the approximation of continuous functions F, defined on a compact Hausdorff space S, whose values F(t), for each t in S, are convex subsets of a normed space E. Both quantitative estimates (in the Hausdorff semimetric) and Bohman-Korovkin type approximation theorems for sequences of monotone operators are obtained.},
author = {Prolla, João},
journal = {Studia Mathematica},
keywords = {Bohman-Korovkin type approximation},
language = {eng},
number = {2},
pages = {175-192},
title = {Approximation of continuous convex-cone-valued functions by monotone operators},
url = {http://eudml.org/doc/215921},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Prolla, João
TI - Approximation of continuous convex-cone-valued functions by monotone operators
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 2
SP - 175
EP - 192
AB - In this paper we study the approximation of continuous functions F, defined on a compact Hausdorff space S, whose values F(t), for each t in S, are convex subsets of a normed space E. Both quantitative estimates (in the Hausdorff semimetric) and Bohman-Korovkin type approximation theorems for sequences of monotone operators are obtained.
LA - eng
KW - Bohman-Korovkin type approximation
UR - http://eudml.org/doc/215921
ER -

References

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  1. [1] R. DeVore, The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Math. 293, Springer, Berlin 1972. Zbl0276.41011
  2. [2] Z. Ditzian, Inverse theorems for multidimensional Bernstein operators, Pacific J. Math. 121 (1986), 293-319. Zbl0581.41023
  3. [3] M. W. Grossman, Note on a generalized Bohman-Korovkin theorem, J. Math. Anal. Appl. 45 (1974), 43-46. Zbl0269.41019
  4. [4] K. Keimel and W. Roth, A Korovkin type approximation theorem for set-valued functions, Proc. Amer. Math. Soc. 104 (1988), 819-824. Zbl0693.47032
  5. [5] O. Shisha and B. Mond, The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1196-1200. Zbl0164.07102
  6. [6] R. A. Vitale, Approximation of convex set-valued functions, J. Approx. Theory 26 (1979), 301-316. Zbl0422.41016

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