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Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

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  • Liang Luo
  • Rizwan Ullah
  • Gul Rahmat
  • Saad Ihsan Butt
  • Muhammad Numan
  • Ming-Sheng Liu

Abstract

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L, we have FM=FYϱ1,0∩FYϱ2,0, where ϱ1 and ϱ2 are positive and ϱ1/ϱ2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

Suggested Citation

  • Liang Luo & Rizwan Ullah & Gul Rahmat & Saad Ihsan Butt & Muhammad Numan & Ming-Sheng Liu, 2021. "Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, March.
    • Handle: RePEc:hin:jjmath:6764280
    DOI: 10.1155/2021/6764280
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