Iterative process with errors to nonlinear Ф-strongly accretive operator equations in arbitrary Banach spaces

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Abstract

Let X be an arbitrary Banach space and T : D(T) ⊂ XX be a Lipschitz ф-strongly accretive operator with domain D(T) and range R(T). The Mann and Ishikawa type iterative sequences with errors which strongly converge to the unique solution of the equation Tx = f under weaker conditions are given. The related results deal with the problems that the Mann and Ishikawa iterative sequences with errors strongly converge to the unique fixed point of Lipschitz ф-hemicontractive operators.

Keywords

Nonlinear ф-strongly accretive operator
ф-hemicontractive operator
Ishikawa type iterative sequence
Arbitrary Banach space

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This project supported by the National Natural Science Foundation of P.R. China.