Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems
Abstract The concept of deferred Nörlund equi-statistical convergence has recently been studied by Srivastaval et al. (see,[19]). In this paper, we have introduced the notion of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence in conjunction with t...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200317 |
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| Sumario: | Abstract The concept of deferred Nörlund equi-statistical convergence has recently been studied by Srivastaval et al. (see,[19]). In this paper, we have introduced the notion of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence in conjunction with the deferred statistical convergence and established a inclusion relation between them. Moreover, we have applied our idea (presumably new) of the deferred equi-statistical convergence to prove a Korovkin-type approximation theorem and demonstrated that our theorem is a non-trivial extension of some well-established Korovkintype approximation theorems which ware proved by some earlier authors. Furthermore, we have established the rate of deferred equistatistical convergence and accordingly proved a theorem. Finally, some concluding remarks and fascinating cases are shown here in support of our definitions and results. |
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