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

• Chidume, C.E. ;
• Nnoli, B.V.C.
• Published : 2002.05.01
• 43 5

#### Abstract

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 $\lambda\$\mid$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.

#### Keywords

demicontractive;condition(A);Banach spaces

#### References

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2. Convergence in norm of modified Krasnoselski–Mann iterations for fixed points of demicontractive mappings vol.217, pp.24, 2011, https://doi.org/10.1016/j.amc.2011.04.068