Rate of convergence for generalized Baskakov operators
نویسندگان
چکیده
منابع مشابه
On the Rate of Convergence by Generalized Baskakov Operators
We firstly construct generalized Baskakov operators V n,α,q (f; x) and their truncated sum B n,α,q (f; γ n , x). Secondly, we study the pointwise convergence and the uniform convergence of the operators V n,α,q (f; x), respectively, and estimate that the rate of convergence by the operators V n,α,q (f; x) is 1/n. Finally, we study the convergence by the truncated operators B n,α,q (f; γ n , x) ...
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In the present paper, we introduce the Durrmeyer variant of Baskakov-Bezier operators Bn,α(f, x), which is the modified form of Baskakov-Beta operators. Here we obtain an estimate on the rate of convergence of Bn,α(f, x) for functions of bounded variation in terms of Chanturiya’s modulus of variation. In the end we also propose an open problem for the readers.
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by replacing the discrete value f(k/n) by the integral (n−1)∫∞ 0 pn,k(t)f (t)dt in order to approximate Lebesgue integrable functions on the interval [0,∞). Some approximation properties of the operators (1.1) were discussed in [6, 7, 8]. In [2, 3], the author defined another modification of the Baskakov operators with the weight functions of Beta operators so as to approximate Lebesgue integra...
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is the Baskakov basis function. Note that (1.1) is well defined, for n ≥ r +2, provided that f(t) = O(tr ) as t → ∞. The operators (1.1) were first introduced by Sahai and Prasad [9]. They termed these operators as modified Lupaş operators. In 1991, Sinha et al. [10] improved and corrected the results of [9] and denoted Ṽn as modified Baskakov operators. The rate of convergence of the operators...
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ژورنال
عنوان ژورنال: Arab Journal of Mathematical Sciences
سال: 2012
ISSN: 1319-5166
DOI: 10.1016/j.ajmsc.2011.08.001