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Bessel statistical convergence: New concepts and applications in sequence theory
Ibrahim S Ibrahim1, Majeed A Yousif1, Pshtiwan Othman Mohammed2
1Department of Mathematics, College of Education, University of Zakho, Zakho, Iraq.
Plos One
|November 14, 2024
Summary
This study introduces Bessel statistical convergence and related sequence concepts. These novel ideas extend approximation theorems, enhancing mathematical analysis with practical applications.
Area of Science:
- Mathematical Analysis
- Sequence Theory
Background:
- Existing sequence theories lack comprehensive frameworks for certain convergence behaviors.
- Approximation theorems require updated methodologies for broader applicability.
Purpose of the Study:
- Introduce novel concepts: Bessel convergence, Bessel boundedness, Bessel statistical convergence, and Bessel statistical Cauchy sequences.
- Extend Korovkin-type approximation theorems using Bessel statistical convergence.
- Demonstrate practical implications through established operators.
Main Methods:
- Development of new definitions and inclusion relations in sequence theory.
- Extension of classical Korovkin-type approximation theorems.
- Application of theorems to Bernstein and Fejér convolution operators.
Main Results:
- Established new inclusion relations and properties for Bessel statistical sequences.
- Successfully extended the first and second Korovkin-type approximation theorems.
- Demonstrated the utility of the extended theorems with concrete examples.
Conclusions:
- The novel Bessel statistical convergence concepts provide a robust framework for sequence analysis.
- Extended approximation theorems offer enhanced analytical capabilities.
- Findings have potential applications in various scientific disciplines requiring sequence analysis.
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