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

Ibrahim S. Ibrahim, Iver Brevik, Ravi P. Agarwal, Majeed A. Yousif, Nejmeddine Chorfi and Pshtiwan Othman Mohammed ()
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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

Mathematics, 2024, vol. 12, issue 23, 1-15

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.

Keywords: Fibonacci sequence; modulus function; weighted Fibonacci statistical convergence; statistical Cauchy; statistical cluster point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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