On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

Abstract

Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.

On Ideal Convergence in Generalized Metric Spaces

“…The concept of ideal convergence, which provides a unifying perspective on various types of convergence related to the concept of statistical convergence, was defined by Kostyrko et al (Kostyrko, Salat, & Wilczynski, 2000). Various studies have conducted with the help of ideal convergence and other types of convergence (see (Demirci, Kişi, & Gürdal, 2023), (Gürdal & Kişi, 2022), (Nabiev, Savaş, & Gürdal, 2019), (Savaş & Gürdal, 2015), (Yamancı & Gürdal, 2013), (Şahiner, Gürdal, & Yiğit, 2011)).…”