$ f $-Statistical convergence on topological modules

Francisco Javier García-Pacheco; Ramazan Kama; Francisco Javier García-Pacheco; Ramazan Kama

doi:10.3934/era.2022110

Electronic Research Archive

2022, Volume 30, Issue 6: 2183-2195. doi: 10.3934/era.2022110

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$ f $-Statistical convergence on topological modules

Francisco Javier García-Pacheco ^{1
,
,},
Ramazan Kama ²

1.
Department of Mathematics, College of Engineering, University of Cadiz, Avda. de la Universidad de Cádiz 10, Puerto Real 11519, Spain
2.
Department of Mathematics and Physical Sciences Education, Faculty of Education, Siirt University, The Kezer Campus, Kezer, 56100-Siirt, Turkey

Received: 29 December 2021 Revised: 08 March 2022 Accepted: 25 March 2022 Published: 19 April 2022

The classical notion of statistical convergence has recently been transported to the scope of real normed spaces by means of the $ f $-statistical convergence for $ f $ a modulus function. Here, we go several steps further and extend the $ f $-statistical convergence to the scope of uniform spaces, obtaining particular cases of $ f $-statistical convergence on pseudometric spaces and topological modules.
- $ f $-statistical convergence,
- statistical convergence,
- uniform space,
- metric space,
- topological module
Citation: Francisco Javier García-Pacheco, Ramazan Kama. $ f $-Statistical convergence on topological modules[J]. Electronic Research Archive, 2022, 30(6): 2183-2195. doi: 10.3934/era.2022110

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Abstract

The classical notion of statistical convergence has recently been transported to the scope of real normed spaces by means of the $ f $-statistical convergence for $ f $ a modulus function. Here, we go several steps further and extend the $ f $-statistical convergence to the scope of uniform spaces, obtaining particular cases of $ f $-statistical convergence on pseudometric spaces and topological modules.

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