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Öğe Approximation by positive linear operators in modular spaces by power series method(Birkhauser Verlag AG, 2017) Taş, Emre; Yurdakadim, TuğbaIn the present paper, we study the problem of approximation to a function by means of positive linear operators in modular spaces in the sense of power series method. Indeed, in order to get stronger results than the classical cases, we use the power series method which also includes both Abel and Borel methods. An application that satisfies our theorem is also provided. © 2017, Springer International Publishing.Öğe Approximation to derivatives of functions by linear operators acting on weighted spaces by power series method(Springer New York LLC, 2016) Taş, Emre; Yurdakadim, TuğbaIn this chapter, using power series method we study some Korovkin type approximation theorems which deal with the problem of approximating a function by means of a sequence of linear operators acting on weighted spaces. © Springer International Publishing Switzerland 2016.Öğe Core Theorems in The Generalized Statistical Sense(2018) Taş, Emre; Yurdakadim, TuğbaThe main purpose of the paper is to give some results concerning with the generalized statistical core of a bounded sequence via B-statistical convergence where B = (Bi) is a sequence of infinite matrices. We characterize the matrix class (stB ?X, Y) for certain sequence spaces X and Y. Here stB is the set of all B-statistically convergent sequences. Finally we answer the multipliers and factorization problem for B-statistically convergent sequences.Öğe Inclusion results on statistical cluster points(Springer Netherlands, 2016) Miller, Harry I.; Wieren, Leila Miller Van; Taş, Emre; Yurdakadim, TuğbaWe study the concepts of statistical cluster points and statistical core of a sequence for A? methods defined by deleting some rows from a nonnegative regular matrix A. We also relate A?-statistical convergence to A?-statistical convergence. Finally we give a consistency theorem for A-statistical convergence and deduce a core equality result.Öğe Korovkin type approximation theorems in weighted spaces via power series method(Element D.O.O., 2018) Taş, Emre; Yurdakadim, Tuğba; Girgin Atlıhan, ÖzlemIn this paper we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space C?1 into a weighted space B?2 with the use of the power series method which includes both Abel and Borel methods. We also consider the rates of convergence of these operators. © 2018, Element D.O.O.. All rights reserved.Öğe Some results for max-product operators via power series method(Univerzita Komenskeho, 2018) Yurdakadim, Tuğba; Taş, EmreIn this paper, we obtain an approximation theorem by max-product operators with the use of power series method which is more effective than ordinary convergence and includes both Abel and Borel methods. We also estimate the error in this approximation. Finally, we provide an example which satisfies our theorem. © 2018, Univerzita Komenskeho. All rights reserved.Öğe The Arzelà-Ascoli theorem by means of ideal convergence(De Gruyter, 2018) Taş, Emre; Yurdakadim, TuğbaIn this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà-Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
