A new iteration process for finite families of generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings |
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Authors: | CE Chidume EU Ofoedu |
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Institution: | 1. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy;2. Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria |
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Abstract: | A new iteration process is introduced and proved to converge strongly to a common fixed point for a finite family of generalized Lipschitz nonlinear mappings in a real reflexive Banach space E with a uniformly Gâteaux differentiable norm if at least one member of the family is pseudo-contractive. It is also proved that a slight modification of the process converges to a common zero for a finite family of generalized Lipschitz accretive operators defined on E. Results for nonexpansive families are obtained as easy corollaries. Finally, the new iteration process and the method of proof are of independent interest. |
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Keywords: | 47H06 47H09 47J05 47J25 |
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