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.
Key words: Orlicz function, weak convergence, lacunary sequence.
Full Text
Article Information
| Title | On Lacunary Weak Convergence of Double Sequences Defined by Orlicz Functions: An Analysis of Topological and Algebraic Structures |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 1, 70-79 |
| DOI | 10.31392/MFAT-npu26_1.2025.07 |
| Milestones | Received 14/01/2025; Revised 17/02/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Binod Chandra Tripathy
Department of Mathematics, Tripura University, 799022, India
Rümeysa Akbıyık
Department of Mathematics, Bartın University, 74100, Bartın, Turkey
Ömer Kişi
Department of Mathematics, Bartın University, 74100, Bartın, Turkey
Citation Example
Binod Chandra Tripathy, Rümeysa Akbıyık, and Ömer Kişi, On Lacunary Weak Convergence of Double Sequences Defined by Orlicz Functions: An Analysis of Topological and Algebraic Structures, Methods Funct. Anal. Topology 31
(2025), no. 1, 70-79.
BibTex
@article {MFAT2100,
AUTHOR = {Binod Chandra Tripathy and Rümeysa Akbıyık and Ömer Kişi},
TITLE = {On Lacunary Weak Convergence of Double Sequences Defined by Orlicz Functions: An Analysis of Topological and Algebraic Structures},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {1},
PAGES = {70-79},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2025.07},
URL = {https://mfat.imath.kiev.ua/article/?id=2100},
}
