A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

Donatus Igbokwe, Oku Ini
DOI: 10.4236/apm.2011.14036                

Abstract

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

Keywords

Implicit Iteration Process, k-Strictly Asymptotically Pseudo-Contractive Maps, Fixed Points

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. O. Osilike, A. Udomene, D. I. Igbokwe and B. G. Akuchu, “Demiclosedness Principle and Convergence Theorems for K-Strictly Asymptotically Pseudocontractive Maps,” Journal of Mathematical Analysis and Applications, Vol. 326, No. 2, 2007, pp. 1334-1345. doi:10.1016/j.jmaa.2005.12.052
[2]	L. Qihou, “Convergence Theorems of the Sequence of Iterates for Asymptotially Demi-contractive and Hemicontractive Mappings,” Nonlinear Analy-sis, Vol. 26, No. 11, 1996, 1835-1842. doi:10.1016/0362-546X(94)00351-H
[3]	M. O. Osilike, S. C. Aniagboso and G. B. Akachu, “Fixed Points of Asymptotically Demicontractive Mapping in Arbitrary Banach Space,” Pan American Mathematical Journal, Vol. 12, No. 2, 2002, pp. 77-88.
[4]	F. E. Browder and W. V. Petryshyn, “Construc-tion of Fixed Points of Nonlinear Mappings in Hilbert Spaces,” Journal of Mathematical Analysis and Applications, Vol. 20, 1967, pp. 197-228. doi:10.1016/0022-247X(67)90085-6
[5]	M. O. Osilike and A. Udomene, “Demiclosedness Principle and Convergence Re-sults for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type,” Journal of Mathematical Analysis and Applications, Vol. 256, 2001, pp. 431-445. doi:10.1006/jmaa.2000.7257
[6]	H. Zhou, “Demiclosedness Principle with Applictions for Asymptotically Pseudocontractions in Hilbert Spaces,” Nonlinear Analysis, Vol. 70, 2009, pp. 3140-3145. doi:10.1016/j.na.2008.04.017
[7]	H. K Xu and R. G. Ori, “An Implicit Iteration Process for Nonexpansive Mappings,” Nu-merical Functional Analysis and Optimization, Vol. 22, 2001, pp. 767-733. doi:10.1081/NFA-100105317
[8]	M. O. Osilike, “Implicit Iteration Process for Common Fixed Point of a Finite Family of Strictly Pseudo-contractive Maps,” Journal of Mathematical Analysis and Applications, Vol. 294, 2004, pp. 73-81. doi:10.1016/j.jmaa.2004.01.038
[9]	Y. Su and S. Li, “Com-posite Implicit Iteration Process for Common Fixed Points of a Finite Family of Strictly Pseudocontractive Maps,” Journal of Mathematical Analysis and Applications, Vol. 320, 2006, pp. 882-891. doi:10.1016/j.jmaa.2005.07.038
[10]	Z. H. Sun, “Strong Con-vergence of an Implicit Iteration Process for a Finite Family of Asymptotically Quasi- nonexpansive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 286, 2003, pp. 351-358. doi:10.1016/S0022-247X(03)00537-7
[11]	M. O. Osilike and B. G. Akuchu, “Common Fixed Points of a Finite Family of Asymptotically Pseudocontractive Maps,” Journal Fixed Points and Applications, Vol. 2, 2004, pp. 81-99. doi:10.1155/S1687182004312027
[12]	C. E. Chidume, “Func-tional Analysis: Fundamental Theorems with Application,” International Centre for Theoretical Physics, Trieste Italy, 1995.
[13]	L. C. Ceng, H. K. Xu and J. C. Yao, “Uniformly Normal Structure and Uniformly Lipschitzian Semigroups,” Nonlinear Analysis, Vol. 73, No. 12, 2010. doi:10.1016/j.na 2010.o7.044.
[14]	W. V. Petryshyn, “A Characterization of Strict Convexity of Banach Spaces and Other Uses of Duality Mappings,” Journal of Functional Analysis, Vol. 6, 1970, pp. 282-291. doi:10.1016/0022-1236(70)90061-3