An Iteration Method for Nonexpansive Mappings in Hilbert Spaces
Lin Wang · Fixed Point Theory and Applications · 2006
Abstract In real Hilbert space "Equation missing", from an arbitrary initial point "Equation missing", an explicit iteration scheme is defined as follows: "Equation missing", where "Equation missing", "Equation missing" is a nonexpansive mapping such that "Equation missing" is nonempty, "Equation missing" is a "Equation missing"-strongly monotone and "Equation missing"-Lipschitzian mapping, "Equation missing", and "Equation missing". Under some suitable conditions, the sequence "Equation missing" is shown to converge strongly to a fixed point of "Equation missing" and the necessary and sufficient conditions that "Equation missing" converges strongly to a fixed point of "Equation missing" are obtained.