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ON I-CONVERGENT DOUBLE SEQUENCE SPACES DEFINED BY A COMPACT OPERATOR AND MODULUS FUNCTIONS
TANWEER JALAL 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.4
In this paper we introduce and study I-convergent double sequence spaces 2SI0 (F, p), 2SI (F, p) and 2SI∞ (F, p) with the help of compact operator T on the real space R and a sequence of modulus functions F = (fij ). We investigate some topological and algebraic properties, and also prove some inclusion relations on these spaces.
Asif Hussain Jan,TANWEER JALAL 강원경기수학회 2023 한국수학논문집 Vol.31 No.3
In this article, we construct lacunary $\Delta^m$-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary $\Delta^m$-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary $\Delta^m$-statistical Cauchy sequences and offered the Cauchy convergence criterion.
On lacunary $\Delta^{m}$-statistical convergence in g-metric spaces
Asif Hussain Jan,TANWEER JALAL 강원경기수학회 2024 한국수학논문집 Vol.32 No.1
The aim of this research is to describe lacunary $\Delta^{m}$-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary $\Delta^{m}$-statistical convergence in g-metric space is established at the end.