Çiğdem Atakut

Approximation by modified Szasz—Mirakjan operators on weighted spaces

The theorems on weighted approximation and the order of approximation of continuous functions by modified Szasz—Mirakjan operators on all positive semi-axis are established.

On Stancu type generalization of q-Baskakov operators

In this paper, we consider a generalization of q-Baskakov operators. We obtain local approximation theorem on the interval [0,~) and also obtain rate of convergence for these new operators in the weighted space.

Stancu type generalization of the Favard–Szàsz operators

Abstract In this paper we establish some approximation properties for a generalized Favard–Szasz type operator.

Approximation by Chlodowsky type Jakimovski-Leviatan operators

We introduce a generalization of the Jakimovski-Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) in [1] and the theorems on convergence and the degree of convergence are established. We also give a Voronovskaya-type theorem. Furthermore, we study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by A.D. Gadjiev and A. Aral (2007) in [9].

Approximation by Kantorovich-Szász Type Operators Based on Brenke Type Polynomials

ABSTRACT In this article, we give a generalization of the Kantorovich-Szász type operators defined by means of the Brenke type polynomials introduced in the literature and obtain convergence properties of these operators by using Korovkin’s theorem. Some graphical examples using the Maple program for this approximation are given. We also establish the order of convergence by using modulus of smoothness and Peetre’s K-functional and give a Voronoskaja type theorem. In addition, we deal with the convergence of these operators in a weighted space.

The generalized Baskakov type operators

The 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.

Approximation properties for generalized Baskakov-type operators

In this paper, we give a generalization of the Baskakov-type operators introduced by Baskakov (Doklady Akademii Nauk SSSR 113:249–251, 1957 (in Russian)) and obtain some direct and inverse results for these new operators.MSC41A35, 41A36

On derivatives of Bernstein type rational functions of two variables

Abstract In this paper the author defines Bernstein type rational functions of two variables and prove the approximation theorems for the derivatives of them.

TOPLAM BİÇİMİNDE DOĞRUSAL OPERATÖRLER AİLESİNİN YAKLAŞIM ÖZELLİKLERİ

Projenin amaci: Toplam bicimde dogrusal operatorler dizilerinin cesitli fonksiyon uzaylarinin normu altinda yaklasim ozelliklerinin arastirilmasi ve bu ozelliklerin uygulamalarinin yapilmasidir.Bunun icin tek ve cok degiskenli fonksiyon uzaylarindadonusum yapan operatorler dizisinin temel yapilari incelenecek ve bu tur operatorlerin olusturulma yontemleri arastirilacaktir. Ayrica polinom bicimde operatorlerin ve toplam formunda ancak polinom biciminde olmayan operatorlerin sinirsiz bolgelerde surekli fonksiyonlar uzayinda, yaklasim ozellikleri incelenecektir.Materyal ve Metod: olarak, Konuyla ilgili basilmis makalelerve kitaplar incelenmis, fonksiyonel analiz, fonksiyonlarin metrigi teorisi ve yaklasimlar teorisinin yontemleri kullanilmistir.Projenin onemi: Genellikle matematiksel literaturde bilinen calismalarda, toplam biciminde pozitif operatorlerle surekli fonksiyonlara yaklasim sonlu kapali aralikta yapilmaktadir.Son yillarda Ankara universitesinde yapilan arastirmalar sonucunda elde edilen bazi neticeler ve bazi teoremler sonucunda, bu yaklasimi sinirsiz bolgelere ve agirlikli normlara tasimaya imkan verecegi dusunulmektedir.Bu calismalar da konunun gelismesine katki da bulunacaktir