The concept of αβ-statistical convergence was introduced and studied by Aktuglu (Korovkin type approximation theorems proved via αβ-statistical convergence, J Comput Appl Math 259: [174][175][176][177][178][179][180][181] 2014). In this work, we generalize the concept of αβ-statistical convergence and introduce the concept of weighted αβ-statistical convergence of order γ , weighted αβ-summability of order γ , and strongly weighted αβ-summable sequences of order γ . We also establish some inclusion relation, and some related results for these new summability methods. Furthermore, we prove Korovkin type approximation theorems through weighted αβ-statistical convergence and apply the classical Bernstein operator to construct an example in support of our result.
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In this study, we introduce the Durrmeyer type Jakimoski-Leviatan operators and examine their approximation properties. We study the local approximation properties of these operators. Further, we investigate the convergence of these operators in a weighted space of functions and obtain the approximation properties. Furthermore, we give a Voronovskaja type theorem for the our new operators.1 n 2 n D 0, there exists a positive constant M such that k L n . ; x/ k x 2 Ä 1 C M.
Abstract. In this paper, we introduce a Stancu type generalization of the q−Favard-Szàsz operators, estimate the rates of statistical convergence and study the local approximation properties of these operators.
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, we provide various approximation results concerning the classical Korovkin theorem via Fibonacci type statistical convergence.
The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space and we give some applications.
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