Abstract.
Consider the Voronovskaja operator A of a sequence of positive linear operators \((L_n )_{n \geq 1} \) and let u(t, x) be the solution of the Cauchy problem for A. In the spirit of Altomare’s theory this solution can be studied by using the semigroup (T(t))t ≥ 0 generated by A and represented in terms of the operators L n .
One associates to A a stochastic equation; its solution can be also used in order to represent u(t, x).
The relations between all these objects are described in the case of the operator A associated with some Meyer-König and Zeller type operators.
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Rasa, I. One-Dimensional Diffusions and Approximation. MedJM 2, 153–169 (2005). https://doi.org/10.1007/s00009-005-0036-8
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DOI: https://doi.org/10.1007/s00009-005-0036-8