Hybrid iterative algorithms for the split common fixed point problems

Jong Soo Jung
2017 Journal of Nonlinear Science and its Applications  
In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) based on the hybrid steepest descent method for solving the split common fixed point problems. We establish the strong convergence of the sequences generated by the proposed algorithms to a solution of the split common fixed point problems, which is also a solution of a certain variational inequality. In particular, the minimum norm solution of the split common fixed point problems is
more » ... problems is obtained. As applications, variational problems and equilibrium problems are considered. c 2017 All rights reserved. Keywords: Split common fixed point problem, firmly nonexpansive mapping, nonexpansive mapping, variational inequality, minimum-norm, ρ-Lipschitzian and η-strongly monotone operator, bounded linear operator, variational problems, equilibrium problems, iterative algorithms.
doi:10.22436/jnsa.010.04.72 fatcat:bdcb4g5eizeurmqkzy5ryq3s4e