ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES - Kişi, Ömer; Cakal, Burak; Gurdal, Mehmet; Kişi, Ömer (Univ Prishtines, 2024)
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.
Keywords: Quaternion Valued G-Metric Space; Ideal Convergence; Ideal Cauchy Sequence