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Weighted almost convergence and related infinite matrices.
Syed Abdul Mohiuddine1, Abdullah Alotaibi1
1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.
Journal of Inequalities and Applications
|January 26, 2018
Summary
This study introduces weighted almost convergence for sequences, proving it forms a BK-space. It also establishes conditions for weighted almost conservative and regular matrices and defines weighted almost A-summable sequences.
Area of Science:
- Mathematical Analysis
- Sequence Spaces
- Functional Analysis
Background:
- The study of convergence and summability of sequences is fundamental in mathematical analysis.
- BK-spaces are a significant class of sequence spaces with applications in functional analysis.
- Weighted convergence and almost convergence are established concepts with existing literature.
Purpose of the Study:
- To introduce and define the concept of weighted almost convergence for sequences.
- To demonstrate that the newly defined sequence space is a BK-space under the sup-norm.
- To investigate weighted almost conservative and regular matrices and weighted almost A-summable sequences.
Main Methods:
- Defining weighted almost convergence for sequences.
- Utilizing the sup-norm to establish the BK-space properties.
- Developing and proving necessary and sufficient conditions for matrix classes.
Main Results:
- The sequence space defined by weighted almost convergence is proven to be a BK-space.
- Necessary and sufficient conditions for weighted almost conservative and regular matrices are derived.
- A novel definition for weighted almost A-summable sequences is introduced and analyzed.
Conclusions:
- Weighted almost convergence provides a new framework within sequence space theory.
- The established BK-space properties and matrix conditions offer tools for further analysis.
- The introduction of weighted almost A-summability opens avenues for future research in summability theory.
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