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On statistical convergence with respect to power series methods

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Abstract

In this paper, we establish a relationship between the concepts of P-strong, P-statistical convergences and P-uniform integrability where P stands for a power series method. We also prove that if a power series method has a summability function, then the space of all P-statistically convergent sequences cannot be endowed with a local convex FK-topology. We finally study P-statistical convergence in a Hausdorff topological space and investigate the relationships among these concepts and weak convergence of Baire measures.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ankara University, Beşevler, 06100, Ankara, Turkey

    M. Ünver

  2. Department of Electrical and Electronics Engineering, Faculty of Engineering, Başkent University, Etimesgut, 06790, Ankara, Turkey

    N. Şahin Bayram

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  1. M. Ünver
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  2. N. Şahin Bayram
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Ünver, M., Bayram, N.Ş. On statistical convergence with respect to power series methods. Positivity 26, 55 (2022). https://doi.org/10.1007/s11117-022-00921-1

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