An iteration method for nonexpansive mappings in Hilbert spaces

作者：Wang Lin^*

来源：Fixed Point Theory and Applications, 2007, 2007(1): 28619.

DOI：10.1155/2007/28619

In real Hilbert space H, from an arbitrary initial point x(0) is an element of H, an explicit iteration scheme is defined as follows: x(n+1) = alpha(n)x(n) + (1 - alpha(n))T(lambda n+1)x(n), n >= 0, where T(lambda n+1)x(n) = Tx(n) - lambda(n+1)mu F(Tx(n)), T : H -> H is a nonexpansive mapping such that F(T) = {x is an element of K : Tx = x} is nonempty, F : H -> H is a eta-strongly monotone and k-Lipschitzian mapping, {alpha(n)} subset of (0, 1), and {lambda(n)} subset of [0,1). Under some suitable conditions, the sequence {x(n)} is shown to converge strongly to a fixed point of T and the necessary and sufficient conditions that {xn} converges strongly to a fixed point of T are obtained.

• 出版日期2007
• 单位南宁师范大学