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On Stability of Iterative Sequences with Error

Author

Listed:
  • Salwa Salman Abed

    (Department of Mathematics, College of Education, Ibn Al-Haitham, University of Baghdad, Baghdad 10001, Iraq)

  • Noor Saddam Taresh

    (Ministry of Higher Education and Scientific Research, Baghdad 10001, Iraq)

Abstract

Iterative methods were employed to obtain solutions of linear and non-linear systems of equations, solutions of differential equations, and roots of equations. In this paper, it was proved that s-iteration with error and Picard–Mann iteration with error converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive mapping. This convergence was almost F -stable and F -stable. Applications of these results have been given to the operator equations F x = f and x + F x = f , where F is a strongly accretive and accretive mappings of X into itself.

Suggested Citation

  • Salwa Salman Abed & Noor Saddam Taresh, 2019. "On Stability of Iterative Sequences with Error," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:765-:d:259308
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    Cited by:

    1. Lu-Chuan Ceng & Meijuan Shang, 2019. "Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems," Mathematics, MDPI, vol. 7(10), pages 1-18, October.

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