7,842 research outputs found
(p,q)-Generalization of Szasz-Mirakyan Operators
In this paper, we introduce new modifications of Szasz-Mirakyan operators
based on (p,q)-integers. We first give a recurrence relation for the moments of
new operators and present explicit formula for the moments and central moments
up to order 4. Some approximation properties of new operators are explored: the
uniform convergence over bounded and unbounded intervals is established, direct
approximation properties of the operators in terms of the moduli of smoothness
is obtained and Voronovskaya theorem is presented. For the particular case p=1,
the previous results for q-Szasz-Mirakyan operators are captured
- …