Generalized Statistical Convergence via Modulus Function in Octonion Valued b-Metric Spaces

Abstract

The key ideas of summability theory have been the subject of extensive investigation in recent years in a variety of metric space extensions. 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. We are prompted by this to study the notions of strong I-Cesàro summability, I-statistical convergence, I-lacunary statistical convergence, and similar notions that respect the modulus function in octonion valued b-metric spaces, an extension of metric spaces. We also examine the connections among these ideas.