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Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps. (English) Zbl 1095.47045
The authors investigate the problem of approximating common fixed points of strictly pseudocontractive operators in a Banach space by a new iteration sequence. Their results improve some results of {\it M. O. Osilike} [J. Math. Anal. Appl. 294, 73--81 (2004; Zbl 1045.47056)].

47J25Iterative procedures (nonlinear operator equations)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
Full Text: DOI
[1] Browder, F. E.; Petryshyn, W. V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. math. Anal. appl. 20, 197-228 (1967) · Zbl 0153.45701
[2] Hicks, T. L.; Kubicek, J. R.: On the Mann iterative process in Hilbert spaces. J. math. Anal. appl. 59, 498-504 (1977) · Zbl 0361.65057
[3] Maruster, S.: The solution by iteration of nonlinear equations. Proc. amer. Math. soc. 66, 69-73 (1977) · Zbl 0355.47037
[4] Osilike, M. O.; Udomene, A.: Demiclosedness principle and convergence results for strictly pseudocontractive mappings of Browder -- petryshyn type. J. math. Anal. appl. 256, 431-445 (2001) · Zbl 1009.47067
[5] Osilike, M. O.: Strong and weak convergence of the Ishikawa iteration methods for a class of nonlinear equations. Bull. korean math. Soc. 37, 117-127 (2000) · Zbl 0956.47021
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[8] Osilike, M. O.; Aniagbosor, S. C.; Akuchu, B. G.: Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces. Pan. amer. Math. J. 12, 77-88 (2002) · Zbl 1018.47047
[9] Xu, H. -K.; Ori, R. G.: An implicit iteration process for nonexpansive mappings. Numer. funct. Anal. optim. 22, 767-773 (2001) · Zbl 0999.47043
[10] Osilike, M. O.: Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps. J. math. Anal. appl. 294, 73-81 (2004) · Zbl 1045.47056
[11] Chang, S. S.: Some problems and results in the study of nonlinear analysis. Nonlinear anal. 30, 4197-4208 (1997) · Zbl 0901.47036
[12] Sun, Z. -H.: Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings. J. math. Anal. appl. 286, 351-358 (2003) · Zbl 1095.47046