Geodesic
Statistical convergence in topological space controlled by modulus function
Ural mathematical journal, Tome 10 (2024) no. 2, pp. 49-59

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he 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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     author = {Parthiba Das and Susmita Sarkar and Prasenjit Bal},
     title = {Statistical convergence in topological space controlled by modulus function},
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     pages = {49--59},
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     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a4/}
}
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Parthiba Das; Susmita Sarkar; Prasenjit Bal. Statistical convergence in topological space controlled by modulus function. Ural mathematical journal, Tome 10 (2024) no. 2, pp. 49-59. http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a4/