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Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation

  • * Corresponding author: Purshottam Narain Agrawal

    * Corresponding author: Purshottam Narain Agrawal
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  • Recently, Karsli [15] estimated the convergence rate of the $ q $-Bernstein-Durrmeyer operators for functions whose $ q $-derivatives are of bounded variation on the interval $ [0, 1] $. Inspired by this study, in the present paper we deal with the convergence rate of a $ q $- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [17], for the functions $ \varphi $ whose $ q $-derivatives are of bounded variation on the interval $ [0, \infty ). $ We present the approximation degree for the operator $ \left( { \mathfrak{S}}_{n, \ell, q}^{(\alpha , \beta )} { \varphi}\right)(\mathfrak{z}) $ at those points $ \mathfrak{z} $ at which the one sided q-derivatives$ {D}_{q}^{+}{ \varphi(\mathfrak{z})\; and\; D} _{q}^{-}{ \varphi(\mathfrak{z})} $ exist.

    Mathematics Subject Classification: 41A25, 41A35.


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