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IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Weak and strong convergence of implicit iterative process for a finite family of asymptotically TJ mappings

Authors and Affiliations

  • Alireza Ghorchizadeh

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Abstract

In this paper we study the weak and strong convergence of implicit iteration process to a common xed point for a nite family of asymptotically TJ mappings in Hilbert spaces. This paper is motivated by [Lin, Lai-Jiu; Chuang, Chih-Sheng; Yu, Zenn-Tsun Fixed point theorems for some new nonlinear mappings in Hilbert spaces, Fixed Point Theory Appl. (2011), 2011:51, 16 pp.].

References

[1] Chang, Shih-sen; Cho, Yeol Je; Zhou, Haiyun, Demi-closed principle and weak convergence problems for asymptotically nonexpansive mappings-,J. Korean Math. Soc. 38 (2001), no. 6, 1245-1260.

[2] Lin, Lai-Jiu; Chuang, Chih-Sheng; Yu, Zenn-Tsun Fixed point theorems for some new nonlinear mappings in Hilbert spaces,Fixed Point Theory Appl. (2011), 2011:51, 16 pp.

[3] Mann, W. Robert, Mean value methods in iteration, Proc.Amer. Math. Soc. 4, (1953). 506-510.

[4] Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73, (1967), 591597.

[5] Takahashi, W., Introduction to nonlinear and convex analysis, Yokohama Publishers, Yokohama, 2009.


How to Cite

Ghorchizadeh, A. (2012). Weak and strong convergence of implicit iterative process for a finite family of asymptotically TJ mappings. International Journal of Applied Mathematical Research, 1(3), 355-359. https://doi.org/10.14419/ijamr.v1i3.188