Regular Article
Ishikawa Iteration Process for Nonlinear Lipschitz Strongly Accretive Mappings

https://doi.org/10.1006/jmaa.1995.1200Get rights and content
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Abstract

Let E = Lp, p ≥ 2 and let T:EE be a Lipschitzian and strongly accretive mapping. Let S:EE be defined by Sx = ƒ − Tx + x. It is proved that under suitable conditions on the real sequences {αn}n=0 and {βn}n=0, the iteration process, x0E, xn+1 = (1 − αn)xn + αnS[(1 − βn)xn + βnSxn], n ≥ 0, converges strongly to the unique solution of Tx = ƒ. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our result gives an affirmative answer to a problem posed by C. E. Chidume (J. Math. Anal. Appl. 151, No. 2 (1990), 453-461).

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