WIJSMAN LACUNARY STATISTICAL CONVERGENCE OF TRIPLE SEQUENCES WITH ORDER α

Abstract

In this Manuscript, we introduce Wijsman’s $p$-lacunary summability of order $\alpha$, Wijsman’s lacunary statistical convergence of order $\alpha$, Hausdorff’s lacunary statistical convergence of order $\alpha$, and Wijsman’s statistical Cauchy for triple set sequences. We embark on a comprehensive exploration of these groundbreaking concepts, delving into their inherent properties, potential interconnections, and ties to established literary ideas. Our examination aims to bring clarity to the characteristics of these innovative notions, uncovering their potential associations. Additionally, we investigate the correlations between these recently introduced concepts and pre-existing notions in the literature.