On Zweier Difierence Ideal Convergence of Double Sequences In Random 2-Normed Spaces

Abstract

Background and Objectives: This article comes from the notion of difference ideal convergence of double sequence space. The notion of zweier convergence was initiated by Şengönül. Kostyrko et al. introduced the notion of I-convergence as a generalization of statistical convergence, which is based on the structure of the ideal I of subsets of natural numbers. Methodology: This stimulus to study some new sequence spaces via convergence by using Zweier operator i.e. convergenceCauchy for double sequences in random 2-normed spaces. Furthermore, inclusion relations between these spaces and some fundamental properties related to these notions. Results: In this section by combining Zweier and generalized difference operators, we define some new notions related to the notion of ideal convergence of double sequences in random 2-normed spaces i.e. ideal convergence, which is a new and interesting idea to work with. We also find some relations related to ideal convergent double sequences in random 2-normed spaces. Also, we find out the relation between ideal convergent and ideal Cauchy double sequences in these spaces. Conclusion: By using Zweier operator via convergence, we define spaces of ideal convergent double sequences in random2-normed spaces and we obtain some basic properties of these notions. These definitions and results provide new tools to deal with the convergence problems of sequences.