Product of deferred Cesàro and deferred weighted statistical probability convergence and its applications to Korovkin-type theorems
In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the idea of statistical convergence for sequences of real numbers, which are defined over a Banach space via the product of deferred Cesàro and deferred weigh...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | article |
| Lenguaje: | EN ES |
| Publicado: |
Pontificia Universidad Javeriana
2020
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/d6f72a7c4679468d982d0241d6a2b3a7 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as
the idea of statistical convergence for sequences of real numbers, which are
defined over a Banach space via the product of deferred Cesàro and deferred
weighted summability means. We first establish a theorem presenting aconnection between them. Based upon our proposed methods, we then prove a
Korovkin-type approximation theorem with algebraic test functions for a
sequence of random variables on a Banach space, and demonstrate that our
theorem effectively extends and improves most (if not all) of the previously
existing results (in classical as well as in statistical versions).
Furthermore, an illustrative example is presented here by means of the
generalized Meyer–König and Zeller operators of a sequence of random
variables in order to demonstrate that our established theorem is
stronger than its traditional and statistical versions. Finally, we
estimate the rate of the product of deferred Cesàro and deferred
weighted statistical probability convergence, and accordingly establish a
new result.
|
|---|