A self-adaptive iterative algorithm for the split common fixed point problems

Abstract

In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get the weak convergence of the proposed algorithm and give applications in the split feasibility problem and the split equality problem. Some numerical experiments are given to illustrate the efficiency of the proposed iterative algorithm. Our results improve and extend the corresponding results announced by many others.

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Correspondence to Jing Zhao.

Additional information

Supported by National Natural Science Foundation of China (No. 61571441) and Scientific Research Project of Tianjin Municipal Education Commission (No. 2018KJ253).

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Cite this article

Zhao, J., Hou, D. A self-adaptive iterative algorithm for the split common fixed point problems. Numer Algor 82, 1047–1063 (2019). https://doi.org/10.1007/s11075-018-0640-x

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Keywords

  • Split common fixed-point problem
  • Iterative algorithm
  • Dual variable
  • Averaged mapping
  • Weak convergence
  • Hilbert space

Mathematics Subject Classification (2010)

  • 47H09
  • 47H10
  • 47J05
  • 54H25