Geodesic
Asymptotics of mean value points in the Schwarz theorem for divided differences
Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 145-174

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We establish inequalities describing the asymptotic behavior of mean value points in the sense of the Schwarz theoremfor general divided differences constructed for a function with a certain growth order at a given point. These inequalities generalize a number of known results, in particular, of ones connected with the asymptotics of Lagrange points in the Taylor formula. 
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     author = {Yu. G. Nikonorov},
     title = {Asymptotics of mean value points in the {Schwarz} theorem for divided differences},
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Yu. G. Nikonorov. Asymptotics of mean value points in the Schwarz theorem for divided differences. Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 145-174. http://geodesic.mathdoc.fr/item/MT_2014_17_1_a6/