STATISTICAL CONVERGENCE IN TOPOLOGICAL SPACE CONTROLLED BY MODULUS FUNCTION

Parthiba Das     (Department of Mathematics, ICFAI University Tripura, Kamalghat, Agartala, 799022, India)
Susmita Sarkar     (Department of Mathematics, ICFAI University Tripura, Kamalghat, Agartala, 799022, India)
Prasenjit Bal     (Department of Mathematics, ICFAI University Tripura, Kamalghat, Agartala, 799022, India)

Abstract


The notion of \(f\)-statistical convergence in topological space, which is actually a statistical convergence's generalization under the influence of unbounded modulus function is presented and explored in this paper. This provides as an intermediate between statistical and typical convergence. We also present many counterexamples to highlight the distinctions among several related topological features. Lastly, this paper is concerned with the notions of \(s^{f}\)-limit point and \(s^{f}\)-cluster point for a unbounded modulus function \(f\).

Keywords


Asymptotic density, \(f\)-statistical convergence, \(f\)-statistical limit point, \(f\)-statistical cluster point

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.2.005

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