Yazar "Yildiz, Sevda" seçeneğine göre listele

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    A THEORY OF VARIATIONS VIA P-STATISTICAL CONVERGENCE
    (Publications L Institut Mathematique Matematicki, 2021) Demirci, Kamil; Djurcic, Dragan; Kocinac, Ljubisa D. R.; Yildiz, Sevda
    We introduce some notions of variation using the statistical convergence with respect to power series method. By the use of the notions of variation, we prove criterions that can be used to verify convergence without using limit value. Also, some results that give relations between P-statistical variations are studied.
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    ABSTRACT KOROVKIN THEOREMS VIA RELATIVE MODULAR CONVERGENCE FOR DOUBLE SEQUENCES OF LINEAR OPERATORS
    (Univ Nis, 2020) Yildiz, Sevda; Demirci, Kamil
    We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators.
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    ABSTRACT KOROVKIN THEORY FOR DOUBLE SEQUENCES VIA POWER SERIES METHOD IN MODULAR SPACES
    (Element, 2019) Dirik, Fadime; Yildiz, Sevda; Demirci, Kamil
    In the present paper, we obtain an abstract version of the Korovkin type approximation theorems for double sequences of positive linear operators on modular spaces in the sense of power series method. We present an example that satisfies our theorem but not satisfies the classical one and also, we study an extension to non-positive operators.
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    Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Boccuto, Antonio; Demirci, Kamil; Yildiz, Sevda
    We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones.
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    Abstract versions of Korovkin theorems on modular spaces via statistical relative summation process for double sequences
    (Tbilisi Centre Math Sci, 2020) Yildiz, Sevda
    In this paper, we studied the abstract versions of Korovkin type approximation theorems via statistical relative A-Summation process in modular spaces for double sequences. Then, we discuss the results which are obtained by special choice of the scale function and the matrix sequences and we give an application that shows our results are stronger than studied before. Finally, we study an extension to non-positive linear operators.
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    Almost A-statistical convergence and approximation theorems
    (Univ Nis, Fac Sci Math, 2025) Demirci, Kamil; Dirik, Fadime; Yildiz, Sevda
    In this paper, we define almost A-statistical convergence via almost regular matrices, which extend the notion of regular matrices, and find its relationship with almost A-summability. Then we study its use in a Korovkin-type approximation theorem. We also construct an example such that our new result works but its classical and statistical versions do not work and a figure will be presented to support our result. Finally, we compute the corresponding rate of almost A-statistical convergence of positive linear operators in two different ways, we have newly defined.
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    An Extension of Korovkin Theorem via P-Statistical A-Summation Process
    (Padova Univ Press, 2023) Demirci, Kamil; Dirik, Fadime; Yildiz, Sevda
    In the present work, we study and prove Korovkin-type approximation theorems for linear operators defined on derivatives of functions by means of A-summation process via statistical convergence with respect to power series method. We give an example that our theorem is stronger. Also, we study the rate of convergence of these operators. Finally, we summarize our results and we show the importance of the study.
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    An extension of Korovkin theorem via power series method
    (Springer Basel Ag, 2022) Yildiz, Sevda; Bayram, Nilay Sahin
    In the present work, using the power series method, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. We also explain that our theorem makes more sense with a striking example. We study the quantitative estimates of linear operators. In the final section, we summarize our new results.
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    Approximation by statistical convergence with respect to power series methods
    (Hacettepe Univ, Fac Sci, 2022) Bayram, Nilay Sahin; Yildiz, Sevda
    In the present work, using statistical convergence with respect to power series methods, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. Then we give an example satisfying our approximation theorem. We study certain rate of convergence related to this method. In the final section we summarize these results to emphasize the importance of the study.
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    Approximation of Abstract Korovkin-Type via Monotone Sublinear Operators: A Power Series Methods and Modified Operators
    (Springer Basel Ag, 2025) Yildiz, Sevda
    This paper introduces a novel framework for approximation through monotone and sublinear operators using the power series method to unify and extend abstract Korovkin-type results. We establish abstract Korovkin-type approximation theorems that are applicable across both a locally compact metric space (as well as a compact metric space) and a compact Hausdorff space. Our results extend previous works by establishing approximation results for nonlinear operators in different function spaces under regular summability methods. We also use a modified modulus of continuity, adapted to the structural properties of the space under consideration, which allows us to derive quantitative estimates. Furthermore, we illustrate the theoretical findings through constructed examples of monotone sublinear operators, including several multivariate extensions developed and analyzed here for the first time.
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    Approximation of matrix-valued functions via statistical convergence with respect to power series methods
    (Springernature, 2022) Demirci, Kamil; Yildiz, Sevda; Cinar, Selin
    In this paper, we deal with an approximation problem for matrix-valued positive linear operators via statistical convergence with respect to the power series method which is a new statistical type convergence. Then, we present an application that shows our theorem is more applicable than the classical one. We also compute the rates of P-statistical convergence of these operators.
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    Approximation Results on an Infinite Interval Based on Power Series Statistical Sense
    (Padova Univ Press, 2025) Yildiz, Sevda; Demirci, Kamil; Dirik, Fadime
    This paper introduces a new approximation theorem, type of Korovkin, for positive linear operators (pLO) defined on the Banach space C-* [0, infinity) comprising all real-valued continuous functions on [0, infinity) that converge to a finite limit as their argument approaches infinity. By applying statistical convergence with respect to power series methods and employing the test functions 1, exp(-u) and exp(-2u), we derive a novel approximation result. Our findings demonstrate that the proposed method outperforms classical and statistical approaches, as illustrated by a concrete example. Furthermore, we explore the rate of convergence associated with this new approximation theorem.
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    Approximation Results via Power Series Method for Sequences of Monotone and Sublinear Operators
    (Springer Basel Ag, 2025) Demirci, Kamil; Dirik, Fadime; Yildiz, Sevda
    In this paper, we use the power series methods to study Korovkin-type approximation theorems for sequences of operators that are monotone and sublinear. It is important to point out that any positive linear operator is monotone sublinear but the converse is not true. We also calculate the rate of convergence in terms of modulus of continuity. Finally, we provide some examples that satisfy our theorems and give quantitative estimates. We also define Bernstein-Chlodovsky-Kantorovich-Choquet (BCKC) polynomial operators similar to those given before and obtain approximation estimate.
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    Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence
    (Amasya University, 2024) Dirik, Fadime; Demirci, Kamil; Yildiz, Sevda
    In this study, we utilize the concept of $\mathcal{I}$-statistical convergence for double sequences to establish a general approximation theorem of Korovkin-type for double sequences of positive linear operators $(PLOs)$ mapping from $H_{\omega }\left( X\right) $ to $C_{B}\left( X\right) $ where $% X=\left
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    Approximation theorems via power series statistical convergence and applications for sequences of monotone and sublinear operators
    (Springer-Verlag Italia Srl, 2025) Yildiz, Sevda; Demirci, Kamil; Dirik, Fadime
    In this paper, we address the problem of extending Korovkin-type approximation theorems to sequences of monotone and sublinear operators via the concept of power series statistical convergence (statistical convergence with respect to power series methods), which is incompatible with statistical convergence and in general a non-matrix method. It is important to emphasise that any positive linear operator is monotone sublinear, but the opposite is not correct. We establish several Korovkin-type theorems under these generalized settings and demonstrate their applicability with concrete examples.
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    Approximation theorems via Pp-statistical convergence on weighted spaces
    (Walter De Gruyter Gmbh, 2024) Yildiz, Sevda; Bayram, Nilay Sahin
    In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for P-p-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces.
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    Approximation via a product (P, Ka)-convergence method on Hω(K)
    (Walter De Gruyter Gmbh, 2026) Cinar, Selin; Yildiz, Sevda; Dirik, Fadime
    This paper presents a Korovkin-type approximation theorem for positive linear operators defined on the space H omega K ${H}_{\omega }\left(K\right)$ with K = 0 , infinity $K=\left[0,\infty \right)$ . The main result is formulated using the concept of (P, K a )-convergence, which is defined as the product of P-statistical convergence and K a -convergence. We provide a constructive example of a sequence of operators that satisfies the conditions of the theorem. The behaviour of the operator in the example has been further illustrated through graphs. Furthermore, we extend our results to the multidimensional case. Finally, we use a modulus of smoothness to calculate the rate of (P, K a )-convergence for this sequence of operators.
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    Approximation via equi-statistical convergence in the sense of power series method
    (Springer-Verlag Italia Srl, 2022) Demirci, Kamil; Dirik, Fadime; Yildiz, Sevda
    In this study, we define a new type of convergence using the notions of statistical convergence in the sense of the power series method and equi-statistical convergence then, we give an example that supports this new definition and after that we use it to prove a Korovkin-type approximation theorem. This theorem is a non-trivial generalization of Korovkin-type approximation theorems that have been studied in earlier papers. Also, we present an example that satisfies our approximation theorem which hasn't satisfied the one studied before. Moreover, we calculate the rate of equi-statistical convergence in the sense of the power series method and then, we prove a Voronovskaya-type approximation theorem. Finally, we summarize our results in the conclusion section.
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    Approximation via Power Series Method in Two-Dimensional Weighted Spaces
    (Malaysian Mathematical Sciences Soc, 2020) Demirci, Kamil; Yildiz, Sevda; Dirik, Fadime
    In this work, we obtain a Korovkin-type approximation theorem for double sequences of real-valued functions by using the power series method in two-dimensional weighted spaces. We also study the rate of convergence by using the weighted modulus of continuity, and in the last section, we present an application that satisfies our new Korovkin-type approximation theorem but does not satisfy classical one.
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    APPROXIMATION VIA STATISTICAL Ka2-CONVERGENCE ON TWO-DIMENSIONAL WEIGHTED SPACES
    (Union Matematica Argentina, 2022) Yildiz, Sevda
    We give a non-regular statistical summability method named statistical K-a(2)-convergence and prove a Korovkin type approximation theorem for this new and interesting convergence method on two-dimensional weighted spaces. We also study the rate of statistical K-a(2)-convergence by using the weighted modulus of continuity and afterwards we present a non-trivial application.