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Deferred Riesz statistical convergence via power series method

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Abstract

In this paper, deferred Riesz statistical convergence as well as \(\hslash \)-deferred Riesz statistical convergence in terms of power series method for real or complex sequences are introduced and studied. Their interconnection with Riesz statistical convergence is explored and illustrative examples in support of our results are presented. Applications of these convergences in the form of a Korovkin-type approximation theorem are established and illustrations demonstrating the superiority of our proven theorem over the classical Korovkin theorem are offered. Finally, the rate of convergence is computed.

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Funding

This work is supported by the Natural Science Foundation of Fujian Province of China (Grant No. 2024J01792).

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Authors and Affiliations

  1. Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000, China

    Qing-Bo Cai

  2. School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, 182320, India

    Samrati Gorka & Kuldip Raj

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  1. Qing-Bo Cai
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  2. Samrati Gorka
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Cai, QB., Gorka, S. & Raj, K. Deferred Riesz statistical convergence via power series method. J. Appl. Math. Comput. 71, 1141–1158 (2025). https://doi.org/10.1007/s12190-024-02283-1

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  • DOI: https://doi.org/10.1007/s12190-024-02283-1

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