A Notion of \(\boldsymbol{\lambda}\)-Fibonacci Statistical Convergence of Sequences of Numbers

A 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.