Riesz lacunary uniform integrability and statistical convergence via power series method

Abstract 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...

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Bibliographic Details
Main Authors: Jun-Jie Quan, Devia Narrania, Kuldip Raj, Qing-Bo Cai
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:https://doi.org/10.1186/s13660-025-03316-4
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Summary:Abstract 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.
ISSN:1029-242X