Yazar "Ulusoy, Gulsum" seçeneğine göre listele
Listeleniyor 1 - 5 / 5
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe Approximation by modified Szasz-Durrmeyer operators(Springer, 2016) Acar, Tuncer; Ulusoy, GulsumThe main goal of this paper is to introduce Durrmeyer modifications for the generalized Szasz-Mirakyan operators defined in (Aral et al., in Results Math 65:441-452, 2014). The construction of the new operators is based on a function which is continuously differentiable times on such that and Involving the weighted modulus of continuity constructed using the function , approximation properties of the operators are explored: uniform convergence over unbounded intervals is established and a quantitative Voronovskaya theorem is given. Moreover, we obtain direct approximation properties of the operators in terms of the moduli of smoothness. Our results show that the new operators are sensitive to the rate of convergence to f, depending on the selection of For the particular case , the previous results for classical Szasz-Durrmeyer operators are captured.Öğe A new construction of Szasz-Mirakyan operators(Springer, 2018) Aral, Ali; Ulusoy, Gulsum; Deniz, EmreThe paper aims to study a generalization of Szasz-Mirakyan-type operators such that their construction depends on a function rho by using two sequences of functions. To show how the function rho play a crucial role in the design of the operator, we reconstruct the mentioned operators which preserve exactly two test functions from the set . We show that these operators provide weighted uniform approximation over unbounded interval. We establish the degree of approximation in terms of a weighted moduli of smoothness associated with the function rho. Also a Voronovskaya type result is presented. Finally some graphical examples of the mentioned operators are given. Our results show that mentioned operators are sensitive or flexible to point of wive of the rate of convergence to f, depending on our selection of rho.Öğe New Integral Type Operators(Univ Nis, Fac Sci Math, 2017) Deniz, Emre; Aral, Ali; Ulusoy, GulsumIn this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0; infinity).Öğe q-Voronovskaya type theorems for q-Baskakov operators(Wiley, 2016) Ulusoy, Gulsum; Acar, TuncerIn the present paper, we prove quantitative q-Voronovskaya type theorems for q-Baskakov operators in terms of weighted modulus of continuity. We also present a new form of Voronovskaya theorem, that is, q-Gruss-Voronovskaya type theorem for q-Baskakov operators in quantitative mean. Hence, we describe the rate of convergence and upper bound for the error of approximation, simultaneously. Our results are valid for the subspace of continuous functions although classical ones is valid for differentiable functions. Copyright (c) 2015 John Wiley & Sons, Ltd.Öğe Simultaneous approximation with generalized Durrmeyer operators(Elsevier Science Inc, 2015) Ulusoy, Gulsum; Deniz, Emre; Aral, AliThe aim of this paper is to obtain some convergence properties of generalized sequences of Ibragimov-Gadjiev-Durrmeyer operators which are a wide class of linear positive operators including many well known linear positive operators. Firstly, the Voronovskaya type theorem in simultaneous approximation is given. Then we present an upper estimate of norm convergence of the derivatives of the operators in quantitative mean in terms of the modulus of continuity. We show several of sequences that can be derived from them by means of a suitable transformation. Some special cases of new operators are presented as examples. (C) 2015 Published by Elsevier Inc.
