On some convergence type in Octonion-valued b-metric spaces

Abstract

This paper will extend some notions, such as convergence, to b-metric spaces with octonion valued b-metric spaces constructed by Qiu et al. Octonion-valued metric spaces are based on modifying the triangle inequality of a semi-metric space by multiplying one side of the inequality by a scalar b. This new generalisation of metric spaces is very interesting since octonions are not even a ring since they do not have the associative property of multiplication and the spaces do not satisfy the standard triangle inequality. Through these concepts, statistical convergence and related concepts are generalised. Properties associated with these concepts are given and the connections between them are established. Moreover, the influence of some structures of octonions on statistical convergence is analysed. Octonion-valued structures extend beyond quaternion-valued frameworks by incorporating non-associative properties, offering a richer setting for studying convergence phenomena. The present work provides new insights by establishing results that are not obtainable in associative settings. These and similar facts make the results obtained in these defined b-metric spaces of particular interest.