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Better error estimation for Szász-Mirakjan-Beta operators. (English) Zbl 1134.41010

Summary: We present a modification of a sequence of mixed summation-integral type operators having Szász and Beta basis functions in summation and integration, the so-called Százs-Mirakjan-Beta operators. Then we show that our modified operators have a better error estimation on the interval \([0,2]\). Furthermore, we give an \(r\)-th order generalization of the modified Százs-Mirakjan-Beta operators and investigate their approximation properties.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
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