Geodesic
Kantorovitch Polynomials Diminish Generalized Length
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 259-262

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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 B n f(x), and they possess similar properties [1]. 
Price, Martin E. Kantorovitch Polynomials Diminish Generalized Length. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 259-262. doi: 10.4153/CMB-1972-047-9
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[1] 1. Lorentz, G. G., Bernstein polynomials, Univ. of Toronto Press, Ontario, 1953. Google Scholar

[2] 2. Goffman, C., Lower-semicontinuity and area functionals. I. The nonparametric case, Rend. Circ. Mat. Palerm. 2, (1953), 203-235. Google Scholar

[3] 3. Hughs, R. E., Length for discontinuous curves, Arch. Rationa. Mech. Anal. 12 (1963), 213-222. Google Scholar

[4] 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

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