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Article An Elaboration of the Cai-Xu Result on (p, q)-integers(Springer Heidelberg, 2020) 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 On the Convergence of the q-bernstein Polynomials for Power Functions(Springer Basel Ag, 2021) Ostrovska, Sofiya; Ozban, Ahmet YasarThe aim of this paper is to present new results related to the convergence of the sequence of the complex q-Bernstein polynomials {B-n,B-q(f(alpha); z)}, where 0 < q not equal 1 and f(alpha) = x(alpha), alpha >= 0, is a power function on [0, 1]. This study makes it possible to describe all feasible sets of convergence K for such polynomials. Specifically, if either 0 < q < 1 or alpha is an element of N-0, then K = C, otherwise K = {0} boolean OR {q(-j)}(j=0)(infinity). In the latter case, this identifies the sequence K = {0} boolean OR {q(-j)}(j=0)(infinity) as the 'minimal' set of convergence for polynomials B-n,B-q(f; z), f is an element of C[0, 1] in the case q > 1. In addition, the asymptotic behavior of the polynomials {B-n,B-q(f(alpha); z)}, with q > 1 has been investigated and the obtained results are illustrated by numerical examples.Article Citation - WoS: 1Citation - Scopus: 1How Do Real and Monetary Integrations Affect Inflation Dynamics?(Elsevier, 2023) Saygili, HulyaThis paper examines the significance of real and monetary integrations for the inflationary dynamics of an emerging country, Turkey. The analysis accounts for 2-digit items of CPI inflation, which can be broadly categorized as tradable versus non-tradable and goods versus services. We find that a fall in the inflation gap between partner countries is mainly related to real integration whereas the co-movement of inflation is prominently driven by monetary policy co-movements. The product-type analysis shows that inflation gap in tradable items between trade partners shrinks and becomes more correlated with the (de)convergence and co-movement of real integration.Article Citation - WoS: 3Citation - Scopus: 3The q-bernstein Polynomials of the Cauchy Kernel With a Pole on [0,1] in the Case q > 1(Elsevier Science inc, 2013) Ostrovska, Sofiya; Ozban, Ahmet YasarThe problem to describe the Bernstein polynomials of unbounded functions goes back to Lorentz. The aim of this paper is to investigate the convergence properties of the q-Bernstein polynomials B-n,B-q(f; x) of the Cauchy kernel 1/x-alpha with a pole alpha is an element of [0, 1] for q > 1. The previously obtained results allow one to describe these properties when a pole is different from q(-m) for some m is an element of {0, 1, 2, ...}. In this context, the focus of the paper is on the behavior of polynomials B-n,B-q(f; x) for the functions of the form f(m)(x) = 1/(x - q(-m)), x not equal q(-m) and f(m)(q(-m)) = a, a is an element of R. Here, the problem is examined both theoretically and numerically in detail. (C) 2013 Elsevier Inc. All rights reserved.Book Part Approximation of Discontinuous Functions by q-bernstein Polynomials(Springer international Publishing Ag, 2016) Ostrovska, Sofia; Ozban, Ahmet YasarThis chapter presents an overview of the results related to the q-Bernstein polynomials with q > 1 attached to discontinuous functions on [0, 1]. It is emphasized that the singularities of such functions located on the set Jq : = {0} boolean OR {q-l}(l=0, infinity), q > 1 are definitive for the investigation of the convergence properties of their q-Bernstein polynomials.Article Citation - WoS: 6Citation - Scopus: 7On the q-bernstein Polynomials of Rational Functions With Real Poles(Academic Press inc Elsevier Science, 2014) Ostrovska, Sofiya; Ozban, Ahmet YasarThe paper aims to investigate the convergence of the q-Bernstein polynomials B-n,B-q(f; x) attached to rational functions in the case q > 1. The problem reduces to that for the partial fractions (x - alpha)(-J), j is an element of N. The already available results deal with cases, where either the pole a is simple or alpha not equal q(-m), m is an element of N-0. Consequently, the present work is focused on the polynomials Bn,q(f; x) for the functions of the form f (x) = (x - q(-m))(-j) with j >= 2. For such functions, it is proved that the interval of convergence of {B-n,B-q(f; x)} depends not only on the location, but also on the multiplicity of the pole - a phenomenon which has not been considered previously. (C) 2013 Elsevier Inc. All rights reserved.
