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Approximation by \((p, q)\)-analogue of Balázs-Szabados operators. (English) Zbl 1499.41086

Summary: In the present paper, we introduce a generalization of Balázs-Szabados operators by means of \((p,q)\)-calculus. We give the rate of convergence of Balázs-Szabados operators based on \((p,q)\)-integrers by using Lipschitz class function and the Peetre’s \(K\)-functional. We give the degree of asymptotic approximation by means of Voronoskaja type theorem. Further, we give some comparisons associated the convergence of Balázs-Szabados, \(q\)-Balázs-Szabados and \((p,q)\)-Balázs-Szabados operators to certain functions by illustrations. Moreover, we investigate the properties of the weighted approximation for these operators.

MSC:

41A36 Approximation by positive operators
41A25 Rate of convergence, degree of approximation
41A35 Approximation by operators (in particular, by integral operators)
41A81 Weighted approximation
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References:

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