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A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions

Author

Listed:
  • Ibrahim S. Ibrahim

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

  • María C. Listán-García

    (Department of Mathematics, Faculty of Science, University of Cádiz, 11510 Cádiz, Spain)

Abstract

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers.

Suggested Citation

  • Ibrahim S. Ibrahim & María C. Listán-García, 2024. "A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions," Mathematics, MDPI, vol. 12(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2718-:d:1468181
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    References listed on IDEAS

    as
    1. Ugur Kadak, 2015. "Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, October.
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