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On (Δm, I)-statistical convergence of order α
Mikail Et1, Abdullah Alotaibi2, S A Mohiuddine2
1Department of Mathematics, Fırat University, 23119 Elazıg, Turkey.
Thescientificworldjournal
|April 2, 2014
Summary
This study introduces new concepts in real sequence analysis: (Δ(m), I)-statistical convergence and strong (Δ(p)(m), I)-Cesàro summability. The research explores the connections between these novel convergence and summability methods for sequences.
Area of Science:
- Real Analysis
- Sequence Theory
- Summability Theory
Background:
- I-convergence of real sequences was established by Kostyrko et al. and Nuray & Ruckle.
- Existing convergence and summability concepts provide a foundation for new theoretical developments.
Purpose of the Study:
- Introduce (Δ(m), I)-statistical convergence of order α.
- Introduce strong (Δ(p)(m), I)-Cesàro summability of order α.
- Investigate the relationship between these new concepts.
Main Methods:
- Definition and theoretical analysis of (Δ(m), I)-statistical convergence.
- Definition and theoretical analysis of strong (Δ(p)(m), I)-Cesàro summability.
- Comparative analysis to establish relationships.
Main Results:
- Novel definitions for (Δ(m), I)-statistical convergence and strong (Δ(p)(m), I)-Cesàro summability are presented.
- The interrelation between these two distinct yet related concepts in sequence theory is explored.
Conclusions:
- The study expands the framework of sequence convergence and summability.
- New theoretical tools are provided for advanced analysis in real analysis and related fields.
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