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Strong convergence of an implicit iteration process for a finite family of strong successively \(\Phi\)-pseudocontractive maps. (English) Zbl 1223.47073

Summary: The aim of this paper is to prove the convergence of an implicit iteration process to a common fixed point for a finite family of strong successive \(\Phi\)-pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of S. S. Chang et al.[J. Math. Anal. Appl. 313, No. 1, 273–283 (2006; Zbl 1086.47044)], N. Shahzad and H. Zegeye [Appl. Math. Comput. 189, No. 2, 1058–1065 (2007; Zbl 1126.65054)] and M. O. Osilike [J. Math. Anal. Appl. 294, No. 1, 73–81 (2004; Zbl 1045.47056)].

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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