ON LACUNARY I –INVARIANT CONVERGENCE OF SEQUENCES IN QUATERNION–VALUED GENERALIZED METRIC SPACES

Abstract

In this study, we explore the concept of lacunary I<inf>?</inf>-convergence of sequences and analyze the relationships between this new convergence concept and the notions of lacunary invariant summability, lacunary strongly s-invariant summability, and lacunary ?-statistical convergence, all of which are defined within quaternion-valued generalized metric spaces. Additionally, our paper aims to introduce the concepts of lacunary I??-convergence in quaternion-valued generalized metric spaces. We then establish the equivalence between lacunary I<inf>?</inf>-convergence and lacunary I??-convergence by providing the definition of property (AP). Furthermore,we introduce lacunary I<inf>?</inf>-Cauchy and lacunary I??-Cauchy sequences, adapting classical theorems to quaternion-valued generalized metric spaces. © 2024 Elsevier B.V., All rights reserved.