A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE MANN SEQUENCE FOR A CLASS OF NONLINEAR OPERATORS

A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE MANN SEQUENCE FOR A CLASS OF NONLINEAR OPERATORS

Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $<x-Tx,j(x-X^8)>\lambda\$\mid$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.

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