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Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions

Author

Listed:
  • Ibrahim S. Ibrahim

    (Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq)

  • Iver Brevik

    (Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway)

  • Ravi P. Agarwal

    (Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Majeed A. Yousif

    (Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq)

  • Nejmeddine Chorfi

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Pshtiwan Othman Mohammed

    (Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq)

Abstract

In this paper, the Fibonacci sequence, renowned for its significance across various fields, its ability to illuminate numerical concepts, and its role in uncovering patterns in mathematics and nature, forms the foundation of this research. This study introduces innovative concepts of weighted density, weighted statistical summability, weighted statistical convergence, and weighted statistical Cauchy, uniquely defined via the Fibonacci sequence and modulus functions. Key theorems, relationships, examples, and properties substantiate these novel principles, advancing our comprehension of sequence behavior. Additionally, we extend the notion of statistical cluster points within a broader framework, surpassing traditional definitions and offering deeper insights into convergence in a statistical context. Our findings in this paper open avenues for new applications and further exploration in various mathematical fields.

Suggested Citation

  • Ibrahim S. Ibrahim & Iver Brevik & Ravi P. Agarwal & Majeed A. Yousif & Nejmeddine Chorfi & Pshtiwan Othman Mohammed, 2024. "Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions," Mathematics, MDPI, vol. 12(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3764-:d:1532489
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