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Generalized Lipschitz Accretive and Pseudo-contractive Mappings

Part of the Lecture Notes in Mathematics book series (LNM, volume 1965)

We have seen in Chapter 11 that several convergence results have been proved on iterative methods for approximating zeros of Lipschitz accretive-type (or, equivalently, fixed points of Lipschitz pseudo-contractive-type) nonlin ear mappings. We have also seen (Chapter 9) that a natural generalization of the class of Lipschitz mappings and the class of mappings with bounded range is that of generalized Lipschitz mappings. In this chapter, by means of an iteration process introduced by Chidume and Ofoedu [152], we prove con vergence theorems for fixed points of generalized Lipschitz pseudo-contractive mappings in real Banach spaces.

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© Springer-Verlag Berlin Heidelberg 2009

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