Applications of relative statistical convergence and associated approximation theorem

Abstract

In this work, we investigate a new type of convergence known as relative statistical convergence through the use of the deferred Nörlund and deferred Riesz means. We demonstrate that the idea of deferred Nörlund and deferred Riesz statistically relative uniform convergence is significantly stronger than deferred Nörlund and deferred Riesz statistically uniform convergence. We provide some interesting examples which explain the validity of the theoretical results and effectiveness of constructed sequence spaces. Furthermore, as an application point of view we prove the Korovkin-type approximation theorem in the context of relative equi-statistical convergence for real valued functions and demonstrate that our theorem effectively extends and most of the earlier existing results. Finally, we present an example involving the Meyer-König-Zeller operator of real sequences proving that our theorem is a stronger approach than its classical and statistical version.

Keywords

• statistical convergence
• deferred nörlund
• deferred riesz
• relative uniform convergence
• pointwise convergence