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On δ -suns

T. D. Narang, Shavetambry Tejpal (2008)

Publications de l'Institut Mathématique

Onesided approximation and real interpolation.

N. Krugljak, E. Matvejev (1997)

Collectanea Mathematica

It is proved that the reiteration theorem is not valid for the spaces Ap (theta,q) defined by V. Popov by means of onesided approximation. It is also proved that a class of cones, defined by onesided approximation of piecewise linear functions on the interval [0,1], is stable for the real interpolation method.

Open problems in constructive function theory.

Baratchart, L., Martínez-Finkelshtein, A., Jimenez, D., Lubinsky, D.S., Mhaskar, H.N., Pritsker, I., Putinar, M., Stylianopoulos, N., Totik, V., Varju, P., Xu, Y. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Optimal cubature formulas in a reflexive Banach space

V. Vaskevich (2003)

Open Mathematics

Sequences of cubature formulas with a joint countable set of nodes are studied. Each cubature formula under consideration has only a finite number of nonzero weights. We call a sequence of such kind a multicubature formula. For a given reflexive Banach space it is shown that there is a unique optimal multicubature formula and the sequence of the norm of optimal error functionals is monotonically decreasing to 0 as the number of the formula nodes tends to infinity.

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