Yazar "Yildiz, Sevda" seçeneğine göre listele
Listeleniyor 1 - 20 / 36
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A THEORY OF VARIATIONS VIA P-STATISTICAL CONVERGENCE(Publications L Institut Mathematique Matematicki, 2021) Demirci, Kamil; Djurcic, Dragan; Kocinac, Ljubisa D. R.; Yildiz, SevdaWe 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.Öğe ABSTRACT KOROVKIN THEOREMS VIA RELATIVE MODULAR CONVERGENCE FOR DOUBLE SEQUENCES OF LINEAR OPERATORS(Univ Nis, 2020) Yildiz, Sevda; Demirci, KamilWe 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.Öğe ABSTRACT KOROVKIN THEORY FOR DOUBLE SEQUENCES VIA POWER SERIES METHOD IN MODULAR SPACES(Element, 2019) Dirik, Fadime; Yildiz, Sevda; Demirci, KamilIn 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.Öğe 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, SevdaWe 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.Öğe Abstract versions of Korovkin theorems on modular spaces via statistical relative summation process for double sequences(Tbilisi Centre Math Sci, 2020) Yildiz, SevdaIn 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.Öğe An Extension of Korovkin Theorem via P-Statistical A-Summation Process(Padova Univ Press, 2023) Demirci, Kamil; Dirik, Fadime; Yildiz, SevdaIn 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.Öğe An extension of Korovkin theorem via power series method(Springer Basel Ag, 2022) Yildiz, Sevda; Bayram, Nilay SahinIn 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.Öğe Approximation by statistical convergence with respect to power series methods(Hacettepe Univ, Fac Sci, 2022) Bayram, Nilay Sahin; Yildiz, SevdaIn 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.Öğe Approximation of matrix-valued functions via statistical convergence with respect to power series methods(Springernature, 2022) Demirci, Kamil; Yildiz, Sevda; Cinar, SelinIn 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.Öğe Approximation Results via Power Series Method for Sequences of Monotone and Sublinear Operators(Springer Basel Ag, 2025) Demirci, Kamil; Dirik, Fadime; Yildiz, SevdaIn 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.Öğe Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence(Amasya University, 2024) Dirik, Fadime; Demirci, Kamil; Yildiz, SevdaIn 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=\leftÖğe Approximation theorems via Pp-statistical convergence on weighted spaces(Walter De Gruyter Gmbh, 2024) Yildiz, Sevda; Bayram, Nilay SahinIn 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.Öğe Approximation via equi-statistical convergence in the sense of power series method(Springer-Verlag Italia Srl, 2022) Demirci, Kamil; Dirik, Fadime; Yildiz, SevdaIn 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.Öğe Approximation via Power Series Method in Two-Dimensional Weighted Spaces(Malaysian Mathematical Sciences Soc, 2020) Demirci, Kamil; Yildiz, Sevda; Dirik, FadimeIn 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.Öğe APPROXIMATION VIA STATISTICAL Ka2-CONVERGENCE ON TWO-DIMENSIONAL WEIGHTED SPACES(Union Matematica Argentina, 2022) Yildiz, SevdaWe 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.Öğe Approximation via statistical relative uniform convergence of sequences of functions at a point with respect to power series method(Springer Heidelberg, 2023) Demirci, Kamil; Dirik, Fadime; Yildiz, SevdaIn the present paper, we generalize the notion of P-statistical convergence and we first define the notion of P-statistical relative uniform convergence of sequences of functions at a point. We demonstrate an approximation theorem for a sequence of functions. Also, we give an example, showing that our result is strict generalization of the corresponding classical ones. In the final section, we study the rates of convergence.Öğe Construction of Bivariate Modified Bernstein-Chlodowsky Operators and Approximation Theorems(Padova Univ Press, 2023) Yildiz, Sevda; Bayram, Nilay SahinIn this paper, we modified Bernstein-Chlodowsky operators via weaker condition than the classical Bernstein-Chlodowsky operators' condition. We get more powerful results than classical ones. We obtain aproximation properties for these positive linear operators and their generalizations in this work. The rate of convergence of these operators is calculated by means of the modulus of continuity and Lipschitz class of the functions off of two variables. Finally, we give some concluding remarks with q-calculus.Öğe DEFERRED NORLUND STATISTICAL RELATIVE UNIFORM CONVERGENCE AND KOROVKIN-TYPE APPROXIMATION THEOREM(Ankara Univ, Fac Sci, 2021) Demirci, Kamil; Dirik, Fadime; Yildiz, SevdaIn this paper, we define the concept of statistical relative uniform convergence of the deferred Norlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.Öğe F-relative A-summation process for double sequences and abstract Korovkin type theorems(Hacettepe Univ, Fac Sci, 2021) Yildiz, SevdaIn this paper, we first introduce the notions of F-relative modular convergence and F-relative strong convergence for double sequences of functions. Then we prove some Korovkin-type approximation theorems via F-relative A-summation process on modular spaces for double sequences of positive linear operators. Also, we present a non-trivial application such that our Korovkin-type approximation results in modular spaces are stronger than the classical ones and we present some estimates of rates of convergence for abstract Korovkin-type theorems. Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.Öğe Ka-Convergence For Double Sequences And Korovkin Type Approximation(Tsing Hua Univ, Dept Mathematics, 2021) Yildiz, SevdaIn this paper, we introduce the idea of K-a-convergence for double sequences. Then, we use this notion to prove a Korovkin type approximation theorem and present an application that satisfies our new main theorem but does not satisfy classical ones. Finally, we study the rate of convergence of positive linear operators.
