A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE MANN SEQUENCE FOR A CLASS OF NONLINEAR OPERATORS
C.E. Chidume, B.V.C. Nnoli · Bulletin of the Korean Mathematical Society · 2002
Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $ eq$ 0 and satisfying the accretive-type condition $ \lambda\ $\mid$ x-Tx\ $\mid$ ^2$ , for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$ . We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.