Year: 2025
Type: article
Abstract: Let ? be a real-or complex-valued function that is measurable in Lebesgue?s sense on some interval (x0, ?), where x0 ? 0. It is known that the existence of ordinary limit of function ? implies the statistical limit of ? . However, the converse implication is not always true. In this study we introduce some Tauberian conditions in terms of the general control modulo of integer order r ? 1. Also we consider the Tauberian conditions of slow decrease and slow oscillation. Under these Tauberian conditions, we obtain the ordinary limit of a function from its statistical limit. The main results generalize some classical type Tauberian theorems given for statistical convergence.
Source: Filomat
DOI: 10.2298/fil2505457o
Authors: Muhammet Okur, İbrahim Çanak
Institutions: Adnan Menderes University, Ege University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412757035