Generalized deferred Cesàro equi-statistical convergence and analogous approximation theorems

• Parida, P. ^[1] ; Paikray, Susanta Kumar ^[2] ; Jena, B. B. ^[2]
  1. [1] Ravenshaw University

     Ravenshaw University

     India

     
  2. [2] Veer Surendra Sai University of Technology

     Veer Surendra Sai University of Technology

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 2, 2020, págs. 317-339
• Idioma: inglés
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• Resumen

  • 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.