Convergence of the q analogue of Szasz-Beta operators
ABSTRACT In the present paper we introduce the q analogue of the well known Szász-Beta operators . We also establish the approximation properties of these operators and estimate convergence results. In the end we propose an open problem.
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- "Weighted approximation. (, ) Let H 2 [0, ∞) be space of all functions f defined on [0, ∞) with the property that |f (x)| ≤ M f (1 + x 2 ), where M f is a constant depending only on f . By C 2 [0, ∞), we denote the subspace of all continuous functions belonging to H 2 [0, ∞). "
ABSTRACT: In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operatorsFilomat 03/2016; · 0.64 Impact Factor
- "qn  qn q 2 n +  qn  qn q n +  qn  qn )[n + p 2] qn q 11 n [n + p 5] qn [n + p 4] qn [n + p 3] qn 4 qn  qn q 5 n [n + p 4] qn [n + p 3] qn ; and C 4 (n; p; q n ) =  qn  qn  qn q 9 n [n + p 5] qn [n + p 4] qn [n + p 3] qn "
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ABSTRACT: In this paper, the explicit estimates of central moments for one kind of exponential-type operators are derived. The estimates play an essential role in studying the explicit approximation properties of this family of operators. Using the proposed method, the results of Ditzian and Totik in 1987, Guo and Qi in 2007, and Mahmudov in 2010 can be improved respectively. Keywordsexponential-type operator–central moment–approximation property–Stirling seriesTransactions of Tianjin University 04/2011; 17(2):85-88. DOI:10.1007/s12209-011-1566-8