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Spaces of ideal convergent sequences
1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.
Thescientificworldjournal
|March 5, 2014
Summary
This study introduces novel sequence spaces defined by ideal convergence and Musielak-Orlicz functions. Researchers explored the topological characteristics of these newly defined mathematical spaces.
Area of Science:
- Real Analysis
- Functional Analysis
- Topology
Background:
- Sequence spaces are fundamental in mathematical analysis.
- Ideal convergence provides a generalized framework for studying convergence properties.
- Musielak-Orlicz functions offer flexibility in defining function spaces.
Purpose of the Study:
- To introduce new sequence spaces utilizing the concepts of ideal convergence.
- To incorporate Musielak-Orlicz functions in the construction of these spaces.
- To investigate and characterize the topological properties of the newly defined sequence spaces.
Main Methods:
- Construction of sequence spaces based on ideal convergence and Musielak-Orlicz functions.
- Application of topological definitions and theorems to analyze the resulting spaces.
- Examination of properties such as completeness, boundedness, and convergence within these spaces.
Main Results:
- The paper defines and establishes the existence of novel sequence spaces.
- Key topological properties of these sequence spaces are analyzed and presented.
- The study provides a foundation for further research into generalized sequence spaces.
Conclusions:
- The introduction of sequence spaces via ideal convergence and Musielak-Orlicz functions expands the landscape of mathematical analysis.
- The identified topological properties offer insights into the structure and behavior of these spaces.
- This work paves the way for exploring advanced concepts and applications in related fields.
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