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Some approximation problems in semi-algebraic geometry

Shmuel Friedland, Małgorzata Stawiska (2015)

Banach Center Publications

In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We...

Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators

Grzegorz Nowak (2008)

Commentationes Mathematicae Universitatis Carolinae

For some classes of functions f locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval [ 0 ; ∞ ) , the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of f is estimated.

Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok (2013)

Mathematica Bohemica

The purpose of this paper is to establish some common fixed point results for f -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).

Some footprints of Marcinkiewicz in summability theory

Ferenc Weisz (2011)

Banach Center Publications

Four basic results of Marcinkiewicz are presented in summability theory. We show that setting out from these theorems many mathematicians have reached several nice results for trigonometric, Walsh- and Ciesielski-Fourier series.

Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi (1999)

Studia Mathematica

An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection q X ( e ) from e to X has fixed cardinality n+1 ( n ⊆ ℕ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection p X ( e ) from e to X where X is a compact subset of .

Some Mean-Value Theorems of the Cauchy Type

Pecaric, Josip, Rodic Lipanovic, Mirna, Srivastava, H. M. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05Some mean-value theorems of the Cauchy type, which are connected with Jensen’s inequality, are given in [2] in discrete form and in [5] in integral form. Several further generalizations and applications of these results are presented here.

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