Eğitim Bilimleri Fakültesi / Faculty of Education
Permanent URI for this collectionhttps://hdl.handle.net/11727/2116
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Item Approximation by Chlodowsky Type Q-Jakimovski-Leviatan Operators(2016) Dalmanoglu, Ozge; Serenbay, Sevilay Kirci; ABF-5851-2020This paper deals with the Chlodowsky type q-Jakimovski-Leviatan operators. We first establish approximation properties and rate of convergence results for these operators. Our main purpose is to give a theorem on the rate of convergence of the rth q-derivative of the operators.Item Rate of Convergence for Generalized Szasz-Mirakyan Operators in Exponential Weighted Space(2017) Serenbay, Sevilay Kirci; Dalmanoglu, Ozge; ABF-5851-2020In the present paper, generalized Szasz-Mirakyan operators in exponential weighted space of functions of one variable are introduced. Using a method given by Rempulska and Walczak, some theorems on the degree of approximation are investigated. Furthermore, a numerical example with an illustrative graphic is given to show comparison for the error estimates of the operators.Item Approximation Theorems for Kantorovich Type Favard-Szasz Operators Based on q-Integers(2017) Dalmanoglu, Ozge; Serenbay, Sevilay Kirci; ABF-5851-2020In this paper we introduce the q-analogue of Kantorovich generalization of Favard-Szasz type operators and investigate their approximation properties. We first give basic convergence results by using Korovkin's Theorem and then estimate the rate of convergence by using modulus of continuity. We also give a local approximation theorem and study weighted approximation properties of these new operators.Item The generalized Baskakov type operators(2014) Serenbay, Sevilay Kirci; Atakut, Cigdem; Buyukyazici, IbrahimThe use of Baskakov type operators is difficult for numerical calculation because these operators include infinite series. Do the operators expressed as a finite sum provide the approximation properties? Furthermore, are they appropriate for numerical calculation? In this paper, in connection with these questions, we define a new family of linear positive operators including finite sum by using the Baskakov type operators. We also give some numerical results in order to compare Baskakov type operators with this new defined operator. (C) 2013 Elsevier B.V. All rights reserved.Item APPROXIMATION BY A GENERALIZED SZASZ TYPE OPERATOR FOR FUNCTIONS OF TWO VARIABLES(2014) Cetin, Nursel; Serenbay, Sevilay Kirci; Atakut, CigdemIn the present paper, we define a new Szasz-Mirakjan type operator in exponential weighted spaces for functions of two variables having exponential growth at infinity using a method given by Jakimovski-Leviatan. This operator is a generalization of two variables of an operator defined by A. Ciupa [1]. In this study, we investigate approximation properties and also estimate the rate of convergence for this new operator.Item Fatou type weighted pointwise convergence of nonlinear singular integral operators Depending on two parameters(2016) Uysal, Gumrah; Serenbay, Sevilay Kirci; ABF-5851-2020In this paper we present some theorems concerning existence and Fatou type weighted pointwise convergence of nonlinear singular integral operators of the form: (T(lambda)f)(x) =integral K-R(lambda)(t-x; f(t))dt, x is an element of R, lambda is an element of Lambda where Lambda not equal empty set is a set of non-negative indices, at a common generalized Lebesgue point of the functions f is an element of L-1,L-empty set (R) and positive weight function empty set. Here, L-1,L-empty set(R) is the space of all measurable functions for which vertical bar f/empty set vertical bar is integrable on R.