Rough $\mathcal{I}$-statistical convergence in a partial metric space
Sukila Khatun, Khairul Hasan, Amar Kumar Banerjee
TL;DR
This work extends convergence theory in partial metric spaces by introducing rough $\mathcal{I}$-statistical convergence and its limit set. It unifies rough statistical and $\mathcal{I}$-convergence concepts, providing definitions, basic properties, and structural results such as closedness of the limit set and a diameter bound $diam(\mathcal{I}-st-LIM^{r}\xi_n) \le 2r+2a$. The analysis includes relationships to $\mathcal{I}$-statistical boundedness and cluster points, offering tools for examining convergence behavior under ideals in partial metric frameworks. The findings advance summability theory in non-metric contexts and may inform applications where self-distances are nonzero and ideal-based convergence is relevant.
Abstract
In this paper we study the notion of rough $\mathcal{I}$-statistical convergence of sequences in a partial metric space as an extension work of both the notions of rough statistical and rough ideal convergence. Here we define rough $\mathcal{I}$-statistical limit set and discuss some relevant properties associated with this set.