ON LACUNARY WEAK CONVERGENCE OF DOUBLE SEQUENCES DEFINED BY ORLICZ FUNCTIONS: AN ANALYSIS OF TOPOLOGICAL AND ALGEBRAIC STRUCTURES

Abstract

This paper provides a comprehensive study of lacunary weak convergence for double sequences, defined through Orlicz functions. It delves into the examination of significant topological and algebraic properties, such as solidity, symmetry, and monotonicity, within the framework of these spaces. To enhance the theoretical foundation, the study includes a range of illustrative examples that highlight instances where certain conditions fail. Furthermore, the paper investigates and establishes inclusion relationships between the newly defined spaces and other existing spaces in the literature. The findings significantly contribute to the broader understanding of sequence spaces, particularly focusing on their structural and convergence characteristics. These results not only enhance the mathematical framework but also provide a foundation for future research into the applications and implications of lacunary weak convergence in double sequences. © (2025), (Institute of Mathematics). All rights reserved.