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

Title & Authors
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.;

Abstract
Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\small{\in}$ E : Tx = x} $\small{\neq}$ 0 and satisfying the accretive-type condition $\lambda\$\small{\mid}$x-Tx\$\small{\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;
Language
English
Cited by
1.
Iterative methods for the computation of fixed points of demicontractive mappings, Journal of Computational and Applied Mathematics, 2010, 234, 3, 861
2.
Convergence in norm of modified Krasnoselski–Mann iterations for fixed points of demicontractive mappings, Applied Mathematics and Computation, 2011, 217, 24, 9864
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