Modulated lacunary statistical convergence of order γ in octonion-valued metric spaces

The primary aim of this paper is to explore novel concepts of convergence and summability for sequences of numbers within the framework of octonion-valued metric spaces, drawing inspiration from modulus functions. Specifically, the study focuses on [Formula: see text]-lacunary statistical convergence of order [Formula: see text] and strong [Formula: see text]-lacunary summability of order [Formula: see text] for sequences of numbers. These innovative concepts are supported by several fundamental theorems, properties, and interrelations.