A SHRINKING PROJECTION METHOD FOR SOLVING THE SPLIT COMMON FIXED POINT PROBLEM IN HILBERT SPACES
Keywords:
Hilbert space, metric projection, monotone operator, nonexpansive mapping, split common fixed point problem
Abstract
We study the split common fixed point problem in two Hilbert spaes. Let H1 and H2 be two real Hilbert spaces. Let S1 : H1 → H1, and S2 : H2 → H2, be two nonexpansive mappings on H1 and H2, respectively. Consider the following problem: find an element x† ∈ H1 such that
x† ∈ Ω := Fix(S1) ∩ T−1( Fix(S2)) ≠ ∅,
where T : H1 → H2 is a given bounded linear operator from H1 to H2.
Using the shrinking projection method, we propose a new algorithm for solving this problem and establish a strong convergence theorem for that algorithm.
điểm /
đánh giá
Published
2019-08-30
Section
NATURAL SCIENCE – ENGINEERING – TECHNOLOGY