Suppose E is a Banach space with certain geometric properties and K is a nonempty closed convex subset of E. We prove that if a certain iterative sequence converges to the unique fixed point of a \(\Phi \)-pseudocontractive mapping \(T:K\rightarrow K\) under certain conditions then such an iterative process can be used to approximate the unique common fixed point of a finite family of \(\Phi \)-pseudocontractive self mappings of K. Our results extend and generalize the results in Chidume (Proc Am Math Soc 120:2641–2649, 1994; Proc Am Math Soc 9:545–551, 1998), Huang (Comput Math Appl 36:13–21, 1998), Liu (Comput Math Appl 45:623–634, 2003), Osilike (Math Anal Appl 200:259–271, 1996; Nonlinear Anal 36:1–9, 1999) and many others.
Common fixed point Iterative approximation \(\Phi \)-pseudocontractive
Mathematics Subject Classification
47H06 47H09 47J05 47J25
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Chidume, C.E.: Global iteration for pseudocontractive maps. Proc. Am. Math. Soc. 9, 545–551 (1998)Google Scholar
Huang, Z.: Approximating fixed points of \(\Phi \)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces. Comput. Math. Appl. 36, 13–21 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
Liu, Zeqing: Iterative solutions of nonlinear equations with \(\Phi \)-strongly accretive operators in uniformly smooth Banach spaces. Comput. Math. Appl. 45, 623–634 (2003)MathSciNetCrossRefzbMATHGoogle Scholar