ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES

Abstract

The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define Zconvergence and Z*-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduceZCauchy and Z*-Cauchy sequences, adapting classically theorems to suit quaternionvalued generalized metric spaces. We also presentZstatistical convergence,Zlacunary statistical convergence, strongZCesa`ro summability, strong Zlacunary summability, [V, )](Z)-summability, and Z-)-statistically convergencein quaternion valued generalized metric spaces, along with their associated properties.