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
Find $$x∗ ∈ \bigcap_{k=1} ^{\infty} Fix (Tk)$$ and $$ ⟨(I − S)x ∗ , x∗ − x⟩ ≤ 0 $$, $$ ∀x ∈ \bigcap_{k=1} ^{\infty} Fix (Tk) $$.