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Some Convergence and Stability Results for the Kirk Multistep and Kirk‐SP Fixed Point Iterative Algorithms

Author

Listed:
  • Faik Gürsoy
  • Vatan Karakaya
  • B. E. Rhoades

Abstract

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk‐SP iterative processes by employing certain contractive‐like operators. Our results generalize and unify some other results in the literature.

Suggested Citation

  • Faik Gürsoy & Vatan Karakaya & B. E. Rhoades, 2014. "Some Convergence and Stability Results for the Kirk Multistep and Kirk‐SP Fixed Point Iterative Algorithms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:806537
    DOI: 10.1155/2014/806537
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    References listed on IDEAS

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    1. Nawab Hussain & Renu Chugh & Vivek Kumar & Arif Rafiq, 2012. "On the Rate of Convergence of Kirk‐Type Iterative Schemes," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Nawab Hussain & Renu Chugh & Vivek Kumar & Arif Rafiq, 2012. "On the Rate of Convergence of Kirk-Type Iterative Schemes," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-22, July.
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    Cited by:

    1. Ting-jian Xiong & Heng-you Lan, 2014. "Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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