Results 1 to 4 of about 5 (4)

Mean value theorems for divided differences and approximate Peano derivatives [PDF]

Mathematica Bohemica, 2009
Summary: Several mean value theorems for higher order divided differences and approximate Peano derivatives are proved.
Mukhopadhyay, S. N., Ray, S.
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The mean value theorem of Flett and divided differences

Journal of Mathematical Analysis and Applications, 2004
Flett's mean value theorem reads as follows: If \(f\) is differentiable on \([a,b]\) and \(f'(a)=f'(b)\), then there exists a point \(c\in(a,b)\) such that \[ f(c)-f(a)=f'(c)(c-a).\tag{11} \] After a careful analysis of divided differences on multiple knots, the authors rewrite as \([a,c,c;f]\) \(=0\) and give condensed representations of other Flett ...
Abel, Ulrich, Ivan, Mircea, Riedel, Thomas   +2 more
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Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions

Journal of Mathematical Analysis and Applications, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Aimin, Cui, Feng, Hu, Zhicheng
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Asymptotics of mean value points in the Schwarz theorem for divided differences

Siberian Advances in Mathematics, 2015
Summary: We establish inequalities describing the asymptotic behavior of mean value points in the sense of the Schwarz theorem for 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
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