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Displaying 81 – 100 of 387

On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function

Luděk Zajíček (1997)

Commentationes Mathematicae Universitatis Carolinae

We improve a theorem of P.G. Georgiev and N.P. Zlateva on Gâteaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly Gâteaux differentiable bump function. In particular, our result implies the following theorem: If $d$ is a distance function determined by a closed subset $A$ of a Banach space $X$ with a uniformly Gâteaux differentiable norm, then the set of points of $X ∖ A$ at which $d$ is not Gâteaux differentiable is not only a first category set, but it is even $σ$ -porous...

On differentiation of metric projections in finite dimensional Banach spaces

Luděk Zajíček (1983)

Czechoslovak Mathematical Journal

On Direct and Converse Theorems in the Theory of Weighted Poynomial Approximation.

Géza Freud (1972)

Mathematische Zeitschrift

On discrepancy theorems with applications to approximation theory

Hans-Peter Blatt (1995)

Banach Center Publications

We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.

On embeddings and traces in Sobolev spaces with weights of power type

Jiří Rákosník (1989)

Banach Center Publications

On embeddings of function classes defined by constructive characteristics

Boris V. Simonov, Sergey Yu. Tikhonov (2006)

Banach Center Publications

In this paper we study embedding theorems for function classes which are subclasses of $L_{p}$ , 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ,β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.