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Topological properties of some sequences defined over 2-normed spaces
Hemen Dutta1, Adem Kilicman2, Omer Altun2
1Department of Mathematics, Gauhati University, Guwahati, 781014 India.
Springerplus
|December 1, 2016
Summary
This study explores novel classes of real number sequences in 2-normed spaces using Orlicz functions and specific sequence spaces. Researchers investigated their properties and relationships for potential future research directions.
Area of Science:
- Real Analysis
- Functional Analysis
- Sequence Spaces
Background:
- 2-normed spaces provide a generalized framework for analyzing sequences.
- Orlicz functions are essential tools in the study of sequence spaces and their properties.
- Paranormed sequence spaces offer a rich structure for mathematical investigation.
Purpose of the Study:
- To define and investigate new classes of real number sequences within 2-normed spaces.
- To analyze the fundamental properties of these newly defined sequence classes.
- To explore the interrelationships between these sequence classes under varying conditions.
Main Methods:
- Utilizing Orlicz functions to construct sequence classes.
- Applying concepts of bounded sequences and multipliers.
- Leveraging the framework of normal paranormed sequence spaces.
- Investigating topological and algebraic properties of the defined spaces.
Main Results:
- Characterization of several new classes of real number sequences.
- Demonstration of inclusion and equality relationships between these classes.
- Identification of specific properties such as completeness and convergence within these spaces.
- Establishment of a foundation for further theoretical development.
Conclusions:
- The study successfully defines and characterizes novel sequence classes in 2-normed spaces.
- Significant relationships and properties of these spaces have been elucidated.
- The findings offer valuable insights and open avenues for advanced research in sequence space theory.
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