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Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we introduce the spaces of vector valued sequences defined by f-statistical convergence and f-statistical summability. We give some topological properties of these spaces. Also, we characterize the Schur property, the Grothendieck property and reflexivity of a normed space in terms of f-statistical convergence.

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Acknowledgements

The author would like to express his deep gratitude to the anonymous learned referees and the editor for their valuable suggestions.

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  1. Department of Mathematics and Physical Sciences Education, Faculty of Education, Siirt University, The Kezer Campus, Kezer, 56100, Siirt, Turkey

    Ramazan Kama

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  1. Ramazan Kama
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Kama, R. Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces. RACSAM 114, 74 (2020). https://doi.org/10.1007/s13398-020-00806-6

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