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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/18
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Article An Elaboration of the Cai-Xu Result on (<i>p</I>, <i>q</I>)-integers(Springer Heidelberg, 2020-02-03) Ostrovska, SofiyaThe investigation of the (p, q)-Bernstein operators put forth the problem of finding the conditions when a sequence of (p, q)-integers tends to infinity. This is crucial for justifying the convergence results pertaining to the (p, q)-operators. Recently, Cai and Xu found a necessary and sufficient condition on sequences {p(n)} and {q(n)}, where 0 < q(n) < p(n) <= 1, to guarantee that a sequence of (p(n), q(n))-integers tends to infinity. This article presents an elaborated version of their result.Article Citation - WoS: 16Citation - Scopus: 19The Sharpness of Convergence Results for <i>q</I>-bernstein Polynomials in The Case <i>q</I> > 1(Springer Heidelberg, 2008-12) Ostrovska, SofiyaDue to the fact that in the case q > 1 the q-Bernstein polynomials are no longer positive linear operators on C[0, 1], the study of their convergence properties turns out to be essentially more difficult than that for q 1. In this paper, new saturation theorems related to the convergence of q-Bernstein polynomials in the case q > 1 are proved.Article Norming Subspaces Isomorphic to <i>l</i><sub>1</sub>(Springer Heidelberg, 2015-04-15) Ostrovska, SofiyaNorming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l(1) provided that the following two conditions are satisfied: (1) X* contains a subspace isomorphic to l(1); and (2) X* contains a separable norming subspace.