Demiclosedness Principle and Convergence Theorems for Strictly Pseudocontractive Mappings of Browder–Petryshyn Type

Abstract

Let E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or lp spaces, 1<p<∞) and K a nonempty closed convex subset of E. Let T:K→K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn (1967, J. Math. Anal. Appl.20, 197–228). It is proved that (I−T) is demiclosed at zero. If F(T)={x∈K:Tx=x}≠∅, weak and strong convergence of the Mann and Ishikawa iteration methods to a fixed point of T is proved.