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Kantorovitch Polynomials Diminish Generalized Length

Published online by Cambridge University Press:  20 November 2018

Martin E. Price
Martin E. Price*
Affiliation:
Wayne State University, Detroit, Michigan
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The Kantorovitch polynomials of a summable function s, defined on [0, 1], are

where

and

They are the analogue for summable functions of the Bernstein polynomials Bnf(x), and they possess similar properties [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 259 - 262
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Lorentz, G. G., Bernstein polynomials, Univ. of Toronto Press, Ontario, 1953.Google Scholar
2. Goffman, C., Lower-semicontinuity and area functionals. I. The nonparametric case, Rend. Circ. Mat. Palerm. 2, (1953), 203-235.Google Scholar
3. Hughs, R. E., Length for discontinuous curves, Arch. Rationa. Mech. Anal. 12 (1963), 213-222.Google Scholar
4. Price, M., On the variation of the Bernstein polynomials of a function of unbounded variation, Pacific J. Math. 27 (1968), 119-122.Google Scholar