| Approximation of Fixed Point and Solution for φ-Hemicontraction and φ-Strongly Quasi-Accretive Operator without Lipschitz Assumption |
| Received:October 11, 1999 |
| Key Words:
φ-strong pseudocontraction φ-strongly accretive operator Ishikawa iteration process Reich's inequality.
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| Abstract: |
| Let X be a real uniformly smooth Banach space and let T:D(T)?X→X be φ-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving φ-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach, Zhou and Jia and others. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2003.01.007 |
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