General Tauberian theorems for the statistically (C, 1) summable integrals
Articles > Article · 2025
Authors: Muhammet Ali Okur, İbrahim ÇANAK
FILOMAT, Journal Indexed in SCI Expanded, International, WoS, 2025, vol 39, pp 1457-1464
DOI: 10.2298/FIL2505457O
Summary
Let f 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 f implies the statistical limit of f. 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.