steklov mean
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2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam N. Agrawal ◽  
Thakur Ashok K. Sinha ◽  
Avinash Sharma

<p style='text-indent:20px;'>The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [<xref ref-type="bibr" rid="b20">20</xref>]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the <inline-formula><tex-math id="M1">\begin{document}$ (2k+2)th $\end{document}</tex-math></inline-formula> order modulus of continuity using Steklov mean.</p>



2005 ◽  
Vol 12 (2) ◽  
pp. 217-228
Author(s):  
Vijay Gupta

Abstract We study some direct results for the recently introduced family of modified Baskakov type operators. In particular, we obtain local direct results on ordinary and simultaneous approximation and an estimation of error for linear combinations in terms of higher order modulus of continuity. We have applied the Steklov mean as a tool for the linear approximating method.



2003 ◽  
Vol 2003 (20) ◽  
pp. 1295-1303 ◽  
Author(s):  
Vijay Gupta ◽  
Prerna Maheshwari ◽  
V. K. Jain

We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.



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