Tchebyshev Systems That Cannot be Transformed Into Markov Systems.
The approximation of functions in the sense of Tchebychev. II
The approximation of functions in the sense of Tchebychev. I
The best approximation of the sinc function by a polynomial of degree with the square norm.
The best L2-approximation by finite sums of functions with separable variables.
The best uniform quadratic approximation of circular arcs with high accuracy
In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples...
The Chebyshev Solution of Certain Matrix Equations.
The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.
The h, p and h-p Versions of the Finite Element Method in 1 Dimension. Part I. The Error Analysis of the p-Version.
The Limit of Non-Linear Chebyshev Approximation on Subsets
The simultaneous nonlinear inequalities problem and applications.
Transformed Linear Chebyshev Approximation.
Transformed Linear Chebyshev Approximation. (Short Communication).
Transitivity of proximinality and norm attaining functionals
We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and...
Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
In this paper we introduce two mappings associated with the lower and upper semi-inner product and and with semi-inner products (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.