Viscosity approximation methods for fixed-points problems
The main result of the paper is: Let \(C\) be a closed convex set of a real Hilbert space \(X\) and \(P:C\rightarrow C\) a nonexpansive operator so that its fixed point set \(S\) is nonempty. Given a sequence of positive real numbers \(\varepsilon_{n}\rightarrow 0\) and a contraction \(\pi:C\rightarrow C,\) the sequence \(x_{n}\in C\) given by the unique fixed point in \(C\) of the contraction \(\frac{1}{1+\varepsilon_{n}}P+\frac{\varepsilon_{n}} {1+\varepsilon_{n}}\pi\) strongly converges to the unique fixed point in \(S\) of the operator proj\(_{S}\circ\pi.\) Applications are given to viscosity principles for optimization problems and inclusions for monotone operators.
viscosity principles for optimization problems
scientific article; zbMATH DE number 1423868