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Bernstein sets with algebraic properties

Marcin Kysiak (2009)

Open Mathematics

We construct Bernstein sets in ℝ having some additional algebraic properties. In particular, solving a problem of Kraszewski, Rałowski, Szczepaniak and Żeberski, we construct a Bernstein set which is a < c-covering and improve some other results of Rałowski, Szczepaniak and Żeberski on nonmeasurable sets.

Best approximation for nonconvex set in q -normed space

Hemant Kumar Nashine (2006)

Archivum Mathematicum

Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q -normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems in best...

Best approximation of coincidence points in metric trees

Bożena Piątek (2008)

Annales UMCS, Mathematica

In this work we present results on fixed points, pairs of coincidence points and best approximation for ε-semicontinuous mappings in metric trees. It is a generalization of the similar properties of upper and almost lower semicontinuous mappings.

Best constants for metric space inversion inequalities

Stephen Buckley, Safia Hamza (2013)

Open Mathematics

For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X o The constant 2 is best possible.

Best simultaneous L p approximations

Yusuf Karakuş (1998)

Czechoslovak Mathematical Journal

In this paper we study simultaneous approximation of n real-valued functions in L p [ a , b ] and give a generalization of some related results.

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