Deferred statistical convergence of sequences in octonion-valued metric spaces

Abstract

By employing octonions, which offer a higher-dimensional and non-associative algebraic structure, octonion-valued metric spaces generalize conventional metric spaces. Every ring forms a module over itself, and every field forms a vector space over itself, as is commonly known. It should be noted, nevertheless, that octonions do not form a module over themselves and so cannot even be regarded as a ring because they lack the multiplicative union condition. The metric spaces we have defined and the findings produced in these spaces are very intriguing because of this aspect. Consequently, various conclusions pertaining to summability theory are examined utilizing some essential concepts associated with these mathematical structures. In particular, we present the concepts of deferred statistical convergence and deferred strong Cesa`ro summability in octonion-valued metric spaces and explore the connections between them. Additionally, we introduce and discuss the concepts of strong deferred invariant convergence, deferred invariant convergence in octonion-valued metric spaces, and deferred invariant statistical convergence.