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Approximation theorems for limit \((p,q)\)-Bernstein-Durrmeyer operator. (English) Zbl 1474.41026

Summary: In the present paper, using the method developed in [the first author, Demonstr. Math. 48, No. 3, 391–403 (2015; Zbl 1321.41035)], we prove the existence of the limit operator of the slight modification of the sequence of \((p,q)\)-Bernstein-Durrmeyer operators introduced recently in [the second author and A. Aral, Facta Univ., Ser. Math. Inf. 31, No. 1, 79–95 (2016; Zbl 1474.41036)]. We also establish the rate of convergence of this limit operator.

MSC:

41A25 Rate of convergence, degree of approximation
41A30 Approximation by other special function classes
41A36 Approximation by positive operators
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