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Öğe Abstract Korovkin theory in modular spaces in the sense of power series method(2018) Yurdakadim, TuğbaIn this paper, using the power series method we obtain an abstract Korovkin type approximation theorem for a sequence of positive linear operators dened on modular spaces.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 inequalities between functionals related to generalized limits(Editura Academiei Romane, 2017) Yurdakadim, Tuğba; Orhan, CihanRecall that A-statistical core theorem determines a class of regular matrices for which lim sup(T x) ? stA ? lim sup x for all x ? m. The main object of this paper is to study an inequality between functionals which is sharper than that of the A-statistical core theorem. We also study the relationship between these functionals and some generalized limits which are called SA-limits and A-Banach limits.Öğe Some Korovkin type results via power series method in modular spaces(Ankara University, 2016) Yurdakadim, TuğbaAbstract. In this paper, we obtain a Korovkin type approximation result for a sequence of positive linear operators deÖned on modular spaces with the use of power series method . We also provide an example which satisfies our theorem.Öğe Some results concerning the summability of spliced sequences(TUBİTAK, 2016) Yurdakadim, Tuğba; Ünver, MehmetA spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral. © Tübi?tak.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 Some results on uniform statistical cluster points(TUBİTAK, 2017) Yurdakadim, Tuğba; Miller-Van-Wieren, LeilaIn this paper, we present some results linking the uniform statistical limit superior and inferior, almost convergence and uniform statistical convergence of a sequence. We also study the relationship between the set of uniform statistical cluster points of a given sequence and its subsequences. The results concerning uniform statistical convergence and uniform statistical cluster points presented here are also closely related to earlier results regarding statistical convergence and statistical cluster points of a sequence. © TÜBI?TAK.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.
