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<p>In this paper, the concepts of Riesz lacunary statistical convergence, Riesz lacunary strong convergence, and Riesz lacunary uniform integrability of real sequences within the framework of power series are introduced and studied. Fundamental relationships among these notions are established, particularly in terms of uniform integrability. A characterization of Riesz lacunary uniform integrability is provided. Furthermore, these definitions by incorporating a modulus function are explored, and significant interrelations among these concepts are investigated.</p>

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Riesz lacunary uniform integrability and statistical convergence via power series method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月28日

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  • Jun-Jie Quan,
  • Devia Narrania,
  • Kuldip Raj,
  • Qing-Bo Cai

摘要

In this paper, the concepts of Riesz lacunary statistical convergence, Riesz lacunary strong convergence, and Riesz lacunary uniform integrability of real sequences within the framework of power series are introduced and studied. Fundamental relationships among these notions are established, particularly in terms of uniform integrability. A characterization of Riesz lacunary uniform integrability is provided. Furthermore, these definitions by incorporating a modulus function are explored, and significant interrelations among these concepts are investigated.