Geodesic
Approximation by the Class of Functions with Bounded Second Derivative
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 583-594

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The paper studies the problem of uniform approximation of a continuous function on a closed interval by the class of functions with bounded second derivative. We prove an estimate of the value of best approximation of the function by this class via its second modulus of continuity. The obtained estimate is sharp for the class of continuous functions.
Keywords: continuous function, best approximation of a function, modulus of continuity, spline, absolutely continuous function, Lipschitz function, divided difference.
Mots-clés : alternance 
@article{MZM_2008_84_4_a9,
     author = {A. V. Mironenko},
     title = {Approximation by the {Class} of {Functions} with {Bounded} {Second} {Derivative}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {583--594},
     publisher = {mathdoc},
     volume = {84},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a9/}
}
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A. V. Mironenko. Approximation by the Class of Functions with Bounded Second Derivative. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 583-594. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a9/