The Moments for the Meyer-König and Zeller Operators

On the Asymptotic Approximation with Bivariate Operators of Bleimann, Butzer, and Hahn

“…Bleimann, Butzer, and Hahn proved that, for bounded f # C[0, ), L [1] n f Ä f as n Ä pointwise on [0, ), the convergence being uniform on each compact subset of [0, ). Furthermore, they found a rate of convergence by estimating |L [1] n ( f (t); x)& f (x)| in terms of the second modulus of continuity of f, where f is assumed to be bounded and uniformly continuous on [0, ). For a growth condition on f which ensures pointwise convergence of L [1] n f as n Ä see [14,Theorem 2.1].…”

“…In 1980 Bleimann, Butzer, and Hahn [10] introduced a sequence of positive linear operators L [1] n defined for any real function f on the interval [0, ) by (L [1] n f )(x)=(1+x) &n :…”

“…Furthermore, they found a rate of convergence by estimating |L [1] n ( f (t); x)& f (x)| in terms of the second modulus of continuity of f, where f is assumed to be bounded and uniformly continuous on [0, ). For a growth condition on f which ensures pointwise convergence of L [1] n f as n Ä see [14,Theorem 2.1]. Several authors [26, 18, 22, 12, 13, 11, 14 16, 8, 19] studied the operators L [1] n in the following (see also [9, pp.…”

ON A SEQUENCE OF KANTOROVICH TYPE OPERATORS VIA RIEMANN TYPE q-INTEGRAL

“…In many papers (see, for instance [1,4,7,11,13,16,21]) the authors studied these operators and some new generalizations of them.…”

A class of linear positive operators in weighted spaces

“…There are many works about these operators (see, for instance [1,3,6,7,8,10,16,18]). The study of approximation theory based on q-integers was firstly started by Phillips in [19].…”