RT journal article
T1 A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions
A1 Ibrahim, I.S.
A1 Listán García, María del Carmen
A2 Matemáticas
K1 Fibonacci sequence
K1 Δ-Fibonacci statistical convergence
K1 strong Δ-Fibonacci summability
K1 Δ-Fibonacci statistical summability
K1 Tauberian conditions
AB The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ-Fibonacci statistical convergence, strong Δ-Fibonacci summability, and Δ-Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers.
PB MDPI
SN 2227-7390
YR 2024
FD 2024-08-30
LK http://hdl.handle.net/10498/35739
UL http://hdl.handle.net/10498/35739
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026