Yazar "Demirci, Kamil" seçeneğine göre listele
Listeleniyor 1 - 20 / 80
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A Korovkin type approximation theorem for double sequences of positive linear operators of two variables in A-statistical sense(Bulletin of the Korean Mathematical Society, 2010) Demirci, Kamil; Dirik, FadimeIn this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from Hw(K) to C(K) via A-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of A -statistical convergence by means of the modulus of continuity.Öğe A KOROVKIN-TYPE APPROXIMATION THEOREM FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS OF TWO VARIABLES IN STATISTICAL A-SUMMABILITY SENSE(Univ Miskolc Inst Math, 2014) Orhan, Sevda; Dirik, Fadime; Demirci, KamilIn this paper, using the concept of statistical A- summability which is stronger than classical convergence and A- statistical convergence, we obtain a Korovkin- type approximation theorem for double sequences of positive linear operators of two variables from H w. K/ to C B. K/. Also, we give an example such that our new approximation result works but its classical and A- statistical cases do not work.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 A-Statistical Korovkin-Type Approximation Theorem For Functions Of Two Variables On An Infinite Interval(Acta Mathematica Universitatis Comenianae, 2012) Demirci, Kamil; Karakuş, SevdaIn this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0;?) x [0;?) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical version.Öğe A-statistical relative modular convergence of positive linear operators(Springer, 2017) Demirci, Kamil; Kolay, BurcakIn this paper, we investigate the problem of statistical approximation to a function f by means of positive linear operators defined on a modular space. Particularly, in order to get stronger results than the classical aspects we mainly use the concept of statistical convergence. Also, a non-trivial application is presented.Öğe A-summation process and Korovkin-type approximation theorem for double sequences of positive linear operators(Walter De Gruyter Gmbh, 2012) Karakus, Sevda; Demirci, KamilThe aim of this paper is to present a Korovkin-type approximation theorem on the space of all continuous real valued functions on any compact subset of the real two-dimensional space by using a A-summation process. We also study the rates of convergence of positive linear operators with the help of the modulus of continuity.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 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 Approximation for periodic functions via statistical ?-convergence(Mathematical Communications, 2011) Demirci, Kamil; Dirik, FadimeIn this study, using the concept of statistical ?-convergence which is stronger than convergence and statistical convergence we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on $C^{\ast }$ which is the space of all $2\pi $-periodic and continuous functions on $\mathbb{R}$, the set of all real numbers. We also study the rates of statistical ?-convergence of approximating positive linear operators.Öğe Approximation for periodic functions via statistical A-summability(Acta Mathematica Universitatis Comenianae, 2012) Demirci, Kamil; Karakuş, Sevda;In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approxima-tion theorem for sequences of positive linear operator de ned on C (R) which is the space of all 2 -periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positive linear operators.Öğe Approximation in statistical sense by n?multiple sequences of fuzzy positive linear operators(Studia Universitatis Babeş-Bolyai -- Series Mathematica, 2012) Demirci, Kamil; Karakuş, SevdaOur primary interest in the present paper is to prove a Korovkin- type approximation theorem for n ? multiple sequences of fuzzy positive linear operators via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.Öğe APPROXIMATION IN STATISTICAL SENSE TO B-CONTINUOUS FUNCTIONS BY POSITIVE LINEAR OPERATORS(Akademiai Kiado Rt, 2010) Dirik, Fadime; Duman, Oktay; Demirci, KamilIn the present work, using the concept of A-statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B-continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.Öğe Approximation in statistical sense to n-variate B-continuous functions by positive linear operators(Versita, 2010) Dirik, Fadime; Demirci, KamilOur primary interest in the present paper is to prove a Korovkintype approximation theorem for sequences of positive linear operators defined on the space of all real valued n-variate B-continuous functions on a compact subset of the real n-dimensional space via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.Öğe Approximation in triangular statistical sense to B-continuous functions by positive linear operators(Sciendo, 2017) Demirci, Kamil; Dirik, Fadime; Okçu, PınarThe main object of this paper is to prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued B-continuous functions on a compact subset of the real line using a new type of statistical convergence of double sequences called triangular-A-statistical convergence for double real sequences. We give an illustrative example in support of our result. Finally, we investigate a rates of triangular-A-statistical convergence of positive linear operators. © 2018, Universitatii Al.I.Cuza din Iasi. All rights reserved.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 On Modular Spaces Via P-Statistical Relative A-Summation Process(2022) Demirci, Kamil; Yıldız, SevdaIn this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some applications to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarksÖğe 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=\left
