A Notion of ?-Fibonacci Statistical Convergence of Sequences of Numbers - Ibrahim, Ibrahim Sulaiman; Listan-Garcia, Maria del Carmen; Colak, Rifat (Maik Nauka/Interperiodica/Springer, 2024)
Fibonacci sequence has profound applications in various fields, including mathematics, computer science, and nature. From modeling natural phenomena to optimizing algorithms and cryptography, Fibonacci sequences play a pivotal role. Moreover, their connection to the golden ratio underscores their relevance in art, architecture, and aesthetics. In this research paper, we introduce new versions of convergence and summability of sequences of numbers with the help of the Fibonacci sequence called lambda-Fibonacci statistical convergence and strong lambda-Fibonacci summability of sequences of numbers by using modulus functions. Also, the definition of lambda- Fibonacci statistical Cauchy of sequences of numbers is given by using modulus functions. These concepts are supported by several of significant theorems and properties in the study. Furthermore, some relations related to these concepts are obtained.
Keywords: Fibonacci sequence; natural density; modulus function; statistical convergence; and phrases; Fibonacci sequence; natural density; modulus function; statistical convergence; lambda-Fibonacci statistical convergence; strong lambda-Fibonacci summability