Browsing by Author "Ostrovska, S."
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Article Citation Count: 4DISTORTION IN THE FINITE DETERMINATION RESULT FOR EMBEDDINGS OF LOCALLY FINITE METRIC SPACES INTO BANACH SPACES(Cambridge Univ Press, 2019) Ostrovska, Sofiya; Ostrovskii, M. I.; MathematicsGiven a Banach space X and a real number alpha >= 1, we write: (1) D(X) <= alpha if, for any locally finite metric space A, all finite subsets of which admit bilipschitz embeddings into X with distortions <= C, the space A itself admits a bilipschitz embedding into X with distortion <= alpha . C; (2) D(X) = alpha(+) if, for every epsilon > 0, the condition D(X) <= alpha + epsilon holds, while D(X) <= alpha does not; (3) D(X) <= alpha(+) if D(X) = alpha(+) or D(X) <= alpha. It is known that D(X) is bounded by a universal constant, but the available estimates for this constant are rather large. The following results have been proved in this work: (1) D((circle plus(infinity)(n= 1) X-n)(p)) <= 1(+) for every nested family of finite-dimensional Banach spaces {X-n}(n=1)(infinity) and every 1 <= p <= 8 infinity. (2) D((circle plus 8(n=1)(infinity)l(infinity)(n) )(p)) = 1(+) for 1 < p < infinity. (3) D(X) <= 4(+) for every Banach space X with no nontrivial cotype. Statement (3) is a strengthening of the Baudier-Lancien result (2008).Article Citation Count: 8On the eigenvectors of the q-Bernstein operators(Wiley, 2014) Ostrovska, Sofiya; Turan, M.; Turan, Mehmet; MathematicsIn this article, both the eigenvectors and the eigenvalues of the q-Bernstein operators have been studied. Explicit formulae are presented for the eigenvectors, whose limit behavior is determined both in the case 01. Because the classical case, where q=1, was investigated exhaustively by S. Cooper and S. Waldron back in 2000, the present article also discusses the related similarities and distinctions with the results in the classical case. Copyright (c) 2013 John Wiley & Sons, Ltd.