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Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null

Xia Li1, Meifang Guo1, Yongfu Su2

  • 1Deprtment of Mathematics and Sciences, Hebei GEO University, Shijiazhuang, 050031 China.

Springerplus
|December 10, 2016
PubMed
Summary

A new hybrid iteration algorithm solves split common fixed point problems in Banach spaces. This method accelerates convergence for finding solutions to split common null point problems, improving prior research.

Keywords:
Duality mappingFixed pointMetric resolventMultidirectional hybrid algorithmSplit common fixed point problemSplit common null point problem

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Area of Science:

  • Functional Analysis
  • Nonlinear Analysis
  • Optimization Theory

Background:

  • Split common fixed point problems are crucial in various fields.
  • Quasi-nonexpansive mappings and maximal monotone operators are key concepts in Banach spaces.
  • Existing iterative algorithms have limitations in convergence speed and applicability.

Purpose of the Study:

  • To introduce a novel multidirectional monotone hybrid iteration algorithm.
  • To establish strong convergence theorems for solving split common fixed point problems.
  • To extend the algorithm's application to split common null point problems.

Main Methods:

  • Development of a new multidirectional monotone hybrid iteration algorithm.
  • Application of convergence analysis techniques in Banach spaces.
  • Proving strong convergence theorems for the proposed algorithm.

Main Results:

  • The proposed algorithm ensures strong convergence for split common fixed point problems.
  • The algorithm is successfully applied to solve split common null point problems.
  • The iteration algorithm demonstrates accelerated convergence properties.

Conclusions:

  • The study presents an effective algorithm for split common fixed point and null point problems.
  • The findings enhance and broaden existing results in fixed point theory.
  • The algorithm offers a faster convergence rate for iterative sequences.