3 results
Search Results
Now showing 1 - 3 of 3
Article Citation - WoS: 1Distortion in the Metric Characterization of Superreflexivity in Terms of the Infinite Binary Tree(Element, 2022) Ostrovska, SofiyaThe article presents a quantitative refinement of the result of Baudier (Archiv Math., 89 (2007), no. 5, 419-429): the infinite binary tree admits a bilipschitz embedding into an arbitrary non-superreflexive Banach space. According to the results of this paper, we can additionally require that, for an arbitrary epsilon > 0 and an arbitrary non-superreflexive Banach space X, there is an embedding of the infinite binary tree into X whose distortion does not exceed 4 + epsilon .Article Citation - WoS: 2Citation - Scopus: 2HOW DO SINGULARITIES OF FUNCTIONS AFFECT THE CONVERGENCE OF q-BERNSTEIN POLYNOMIALS?(Element, 2015) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Turan, MehmetIn this article, the approximation of functions with a singularity at alpha is an element of (0, 1) by the q-Bernstein polynomials for q > 1 has been studied. Unlike the situation when alpha is an element of (0, 1) \ {q(-j)} j is an element of N, in the case when alpha = q(-m), m is an element of N, the type of singularity has a decisive effect on the set where a function can be approximated. In the latter event, depending on the types of singularities, three classes of functions have been examined, and it has been found that the possibility of approximation varies considerably for these classes.Article Citation - WoS: 18Citation - Scopus: 21TRIPLED BEST PROXIMITY POINT THEOREM IN METRIC SPACES(Element, 2013) Cho, Yeol Je; Gupta, Animesh; Karapinar, Erdal; Kumam, Poom; Sintunavarat, WutipholThe purpose of this article is to first introduce the notion of tripled best proximity point and cyclic contraction pair. We also establish the existence and convergence theorems of tripled best proximity points in metric spaces. Moreover, we apply our results to setting of uniformly convex Banach space. Finally, we obtain some results on the existence and convergence of tripled fixed point in metric spaces and give illustrative examples of our theorems.
