Abstract
In this paper, a new ( p,q ) -analogue of the Balázs–Szabados operators is defined. Moments up to the fourth order are calculated, and second order and fourth order central moments are estimated. Local approximation properties of the operators are examined and a Voronovskaja type theorem is given.
Highlights
Bernstein type rational functions are defined and studied by Balázs in 1975 as follows: n kRn(f ; x) = (1 + anx)n k=0 f bn n kk (n = 1, 2, . . .), where f is a real- and single-valued function defined on the interval [0, ∞), an and bn are real numbers which are appropriately selected and do not depend on x
Several q-generalizations of Balázs–Szabados operators have been recently studied by Hamal and Sabancigil [14], Doğru [10], and Özkan [31]
The Balázs–Szabados operator based on the q-integers were defined by Mahmudov in [21] as follows: n
Summary
1 Introduction Bernstein type rational functions are defined and studied by Balázs in 1975 as follows (see [6]): n k Several q-generalizations of Balázs–Szabados operators have been recently studied by Hamal and Sabancigil [14], Doğru [10], and Özkan [31]. The Balázs–Szabados operator based on the q-integers were defined by Mahmudov in [21] as follows: n
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