Abstract
We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ‐pseudocontractive mappings in normed linear spaces. Our results extend and improve the corresponding results of Xu, 1998, Kim et al., 2009, Ofoedu, 2006, Chidume and Zegeye, 2004, Chidume, 2001, Chang et al. 2002, Liu, 1995, Hirano and huang, 2003, C. E. Chidume and C. O. Chidume, 2005, and huang, 2007.
Highlights
Let E be a real normed linear space, E∗ its dual space, and J : E → 2E∗ the normalized duality mapping defined byJ x f ∈ E∗ : x, f x · f f2, 1.1 where ·, · denotes the generalized duality pairing
We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ-pseudocontractive mappings in normed linear spaces
The purpose of this paper is that we obtain the convergence result of the Mann iteration with errors, and we prove the equivalence of convergence between the Ishikawa iteration with errors defined by 1.10 and the Mann iteration with errors defined by 1.11
Summary
We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ-pseudocontractive mappings in normed linear spaces. Our results extend and improve the corresponding results of Xu, 1998, Kim et al, 2009, Ofoedu, 2006, Chidume and Zegeye, 2004, Chidume, 2001, Chang et al 2002, Liu, 1995, Hirano and huang, 2003, C. E. Chidume and C.
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