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Some Approximation Properties of Modified Jain-Beta Operators

机译:修正的Jain-Beta算子的一些逼近性质

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摘要

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parametersα,β, andγand discuss Voronovskaja asymptotic formula.
机译:Jain,1972年就考虑了Szász-Mirakyan算子的泛化。使用这些广义算子,我们引入了新的正线性算子序列,它们是Jain算子具有某些Beta基函数的加权函数的整数形式。对于这些新算子,研究了近似性质,收敛速度,加权近似定理和更好的近似。最后,我们对具有三个参数α,β和γ的Jain-Beta算子进行了推广,并讨论了Voronovskaja渐近公式。

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