Functional Analysis

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• \Bibitem{1} \by Sibel Ersan Ogun Dogru \paper Statistical approximation properties of q-Bleimann, Butzer and Hahn operators \paperinfo The main aim of this study is to introduce a new generalization of q-Bleimann, Butzer and Hahn operators and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical BBH operators. The second aim of this study is to construct a bivariate generalization of the operator and also obtain the statistical approximation properties. \jour Mathematical and Computer Modelling \yr 2009 \vol 49 \pages 1595-1606
• \Bibitem{2} \by Sibel Ersan Huseyin Cakalli \paper Ward Continuity in 2-Normed Spaces \paperinfo In this paper, we introduce and investigate the concept of ward continuity in 2-normed spaces. Some other kinds of continuities are also introduced, and interesting theorems are proved in 2-normed spaces. \jour Filomat \yr 2015 \vol 29 \issue 7 \pages 1507-1513
• \Bibitem{3} \by Huseyin Cakalli Sibel Ersan \paper New Types of Continuity in 2-Normed Spaces \paperinfo A sequence (xn) of points in a 2-normed space X is statistically quasi-Cauchy if the sequence of difference between successive terms statistically converges to 0. In this paper we mainly study statistical ward continuity, where a function f defined on a subset E of X is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in E. Some other types of continuity are also discussed, and interesting results related to these kinds of continuity are obtained in 2-normed space setting. \jour Filomat \yr 2016 \vol 30 \issue 3 \pages 525-532
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