Estimation on the Convergence of the Semi-Exponential Szász-Mirakyan-Kantorovich Operators
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The approximation rate of some Szász-Mirakyan-Kantorovich operators for some absolutely continuous functions is obtained. Firstly, the author introduces the new Szász-Mirakyan operators of the integral form. After a simple calculation, the first and second order central moment of the new integral form operators are given. Late, using analysis techniques the approximation theorem of the new operators is decomposed into several parts. Then, each estimate is calculated. Lastly, an asymptotically optimal estimate is obtained as same as the classical method of Bojanic and Cheng. The conclusion drawn in this article extends the research findings of Agrawal and Gupta.
Szász-Mirakyan-Kantorovich operators; Approximation rate; Bounded variation