The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping
Jarosław Górnicki · Fixed Point Theory and Applications · 2009
Abstract The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let "Equation missing" be a Hilbert space, let "Equation missing" be a nonempty bounded closed convex subset of "Equation missing" and let "Equation missing" be a strongly ergodic matrix. If "Equation missing" is a lipschitzian mapping such that "Equation missing", then the set of fixed points "Equation missing" is a retract of "Equation missing". This result extends and improves the corresponding results of [7, Corollary 9] and [8, Corollary 1].