Approximation properties of a generalization of Bleimann, Butzer and Hahn operators.
In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate -Bernstein polynomials for a function analytic in the polydisc for arbitrary fixed . We give quantitative Voronovskaja type estimates for the bivariate -Bernstein polynomials for . In the univariate case the similar results were obtained by S. Ostrovska: -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution...
We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.
MSC 2010: 41A25, 41A35
In this note we give some direct and inverse approximation theorems for the Picard singular integral in the exponential weighted spaces and some generalized Hölder spaces.
We obtain modular convergence theorems in modular spaces for nets of operators of the form , w > 0, s ∈ G, where G and H are topological groups and is a family of homeomorphisms Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.