A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces

Abstract

The applications of a Fibonacci sequence in mathematics extend far beyond their initial discovery and theoretical significance. The Fibonacci sequence proves to be a versatile tool with real-world implications and the practical utility of manifests in various fields, including optimization algorithms, computer science and finance. In this research paper, we introduce new versions of convergence and summability of sequences in normed spaces with the help of the Fibonacci sequence called weak Fibonacci phi-lacunary statistical convergence and weak Fibonacci phi-lacunary summability, where phi is a modulus function under certain conditions. Furthermore, we obtain some relations related to these concepts in normed spaces.