A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces
Let H H be a real Hilbert space. Suppose that T T is a nonexpansive mapping on H H with a fixed point, f f is a contraction on H H with coefficient ??(0,1) ? ? ( 0 , 1 ) , F:H?H F : H ? H is a k k -Lipschitzian and ? ? -strongly monotone operator with k>0,?>0 k > 0 , ? > 0 , and A:H?H A : H ? H is a strongly positive bounded linear operator with coefficient ? ? ? ( 1 , 2 ) . Let 0 < ? < 2 ? / k 2 , 0 < ? < ? ( ? ? ? k 2 2 ) / ? = ? / ? . It is shown that the sequence {xn} { x n } generated by the following general composite iterative method:
nonexpansive mappings fixed point composite iterative method variational inequality projection viscosity approximation