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Area of Science:

  • Mathematics
  • Number Theory
  • Approximation Theory

Background:

  • Statistical convergence is a key concept in number theory.
  • The Korovkin theorem is fundamental in approximation theory.
  • Fibonacci sequences have unique mathematical properties.

Purpose of the Study:

  • To define and investigate a novel statistical convergence using Fibonacci sequences.
  • To explore the foundational characteristics of this new convergence type.
  • To extend the classical Korovkin theorem using Fibonacci-based statistical convergence.

Main Methods:

  • Definition of statistical convergence with Fibonacci sequences.
  • Analysis of fundamental properties of the defined convergence.
  • Application of Fibonacci type statistical convergence to Korovkin's theorem.

Main Results:

  • A new definition of statistical convergence involving Fibonacci numbers is established.
  • Key properties of Fibonacci statistical convergence are analyzed.
  • Approximation results are derived by extending the Korovkin theorem.

Conclusions:

  • The study successfully introduces and analyzes Fibonacci statistical convergence.
  • New approximation results are obtained, extending existing theorems.
  • This work contributes to the understanding of convergence in mathematical analysis.