He Songnian, Guo Jun, "Algorithms for Finding the Minimum Norm Solution of Hierarchical Fixed Point Problems," WSEAS Transactions on Mathematics, vol. 12, pp. -, 2013, DOI:
He Songnian, Guo Jun. Algorithms for Finding the Minimum Norm Solution of Hierarchical Fixed Point Problems.
WSEAS Transactions on Mathematics. 2013;12:-.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Algorithms for Finding the Minimum Norm Solution of Hierarchical Fixed Point Problems
Authors: ,
Abstract: Let C be a nonempty closed convex subset of a real Hilbert space H, $$\lbrace Tk
\rbrace _{k=1} ^{\infty}$$ : C → C an infinite family of nonexpansive mappings with the nonempty set of common fixed points $$\bigcap_{k=1} ^{\infty} Fix (Tk)$$ and S : C → C a nonexpansive mapping. In this paper, we introduce an explicit algorithm with strong convergence for finding the minimum norm solution of the following hierarchical fixed point problem <br><br> Find $$x∗ ∈ \bigcap_{k=1} ^{\infty} Fix (Tk)$$ and $$ ⟨(I − S)x ∗ , x∗ − x⟩ ≤ 0 $$, $$ ∀x ∈ \bigcap_{k=1} ^{\infty} Fix (Tk) $$.
Keywords:
Hierarchical fixed point, Iterative algorithm, Variational inequality, Minimum norm, Strong convergence
Pages: - WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 12, 2013DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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