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Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method

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  • Faizan Ahmad Khan
  • Valerii Obukhovskii

Abstract

The main intent of this article is to innovate a new iterative method to approximate fixed points of contraction and nonexpansive mappings. We prove that the new iterative method is stable for contraction and has a better rate of convergence than some distinctive iterative methods. Furthermore, some convergence results are proved for nonexpansive mappings. Finally, the solution of a nonlinear fractional difference equation is approximated via the proposed iterative method. Some numerical examples are constructed to support the analytical results and to illustrate the efficiency of the proposed iterative method.

Suggested Citation

  • Faizan Ahmad Khan & Valerii Obukhovskii, 2022. "Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, December.
    • Handle: RePEc:hin:jjmath:6962430
    DOI: 10.1155/2022/6962430
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