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

Let E be a real q-uniformly smooth Banach space which is also uniformly convex Žfor 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 Ž1967, J. Math. Anal. Appl. 20, 197 228.. It is proved that Ž I T. is demiclosed at zero. If FŽT. x K : Tx x4 , weak and strong convergence of the Mann and Ishikawa iteration methods to a fixed point of T is proved