Geodesic
Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings in Banach spaces
Dong, Qiao-Li1 ; He, Songnian1 ; Deng, Bin-Chao2
1 College of Science, Civil Aviation University of China, Tianjin 300300, China
2 Technical economy and management specialty, School of Management, Tianjin University, Tianjin 300072, China
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 3, p. 232-242.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we consider a general iterative scheme to approximate a common fixed point for a finite family of asymptotically quasi-nonexpansive mappings. Several strong and weak convergence results are presented in Banach spaces and an finite family of asymptotically quasi-nonexpansive mappings is constructed. Our results generalize and extend many known results in the current literature.
DOI : 10.22436/jnsa.005.03.07
Classification : 47H05, 47H07, 47H10
Keywords: Modified Mann and Ishikawa iterations, Asymptotically quasi-nonexpansive mappings, Common fixed points, Weak and strong convergence, Uniformly convex Banach spaces.

Dong, Qiao-Li 1 ; He, Songnian 1 ; Deng, Bin-Chao 2

1 College of Science, Civil Aviation University of China, Tianjin 300300, China
2 Technical economy and management specialty, School of Management, Tianjin University, Tianjin 300072, China 
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Dong, Qiao-Li; He, Songnian; Deng, Bin-Chao. Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings in Banach spaces. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 3, p. 232-242. doi : 10.22436/jnsa.005.03.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.03.07/

[1] Goebel, K.; Kirk, W. A. A fixed point theorem for asymptotically non-expansive mappings, Proc. Amer. Math. Soc., Volume 35 (1972), pp. 171-174

[2] Bose, S. C. Weak convergence to the fixed point of an asymptotically nonexpansive map, Proc. Amer. Math. Soc., Volume 68 (1978), pp. 305-308

[3] Khan, S. H.; W. Takahasi Approximating common fixed points of two asymptotically nonexpanisve mappings, Sci. Math. Jpn., Volume 53 (2001), pp. 143-148

[4] Ceng, L. C.; Cubiotti, P.; Yao, J. C. Appoximation of common fixed points of families of nonexpansive mappings, Taiwanese J. Math., Volume 12 (2008), pp. 487-500

[5] Yao, Y.; Yao, J. C.; Zhou, H. Appoximation methods for common fixed points of infinite countable family of nonexpansive mappings, Comput. Math. Appl. , Volume 53 (2007), pp. 1380-1389

[6] Dong, Q. L.; He, S.; Su, F. Strong convergence of an iterative algorithm for an infinite family of strict pseudo- contractions in Banach spaces , Appl. Math. Comput., Volume 216 (2010), pp. 959-969

[7] Z. H. Sun Strong convergence of an implicit iteration process for a finite family of asymptotically quasi- nonexpansive mappings, J. Math. Anal. Appl., Volume 286 (2003), pp. 351-358

[8] Xu, H. K.; Ori, R. G. An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim., Volume 22 (5-6) (2001), pp. 767-773

[9] Shahzad, N.; Udomene, A. Approximating common fixed points of two asymptotically quasi-nonexpanisve mappings in Banach spaces, Fixed Point Theory Appl., Article ID 18909 (2006), pp. 1-10

[10] Fukhar-ud-din, H.; Khan, S. H. Convergence of iterates with errors of asymp , J. Math. Anal. Appl., Volume 328 (2007), pp. 821-829

[11] Khan, A. R.; Domlo, A. A.; Fukhar-ud-din, H. Common fixed point Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., Volume 341 (2008), pp. 1-11

[12] Schu, J. Weak and strong convergence to fixed points of asymptotically nonexpansive mappings , Bull. Austral. Math. Soc., Volume 43 (1991), pp. 153-159

[13] Tan, K. K.; Xu, H. K. Fixed point iteration process for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., Volume 122 (1994), pp. 733-739

[14] Xu, B.; Noor, M. A. Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., Volume 267 (2002), pp. 444-453

[15] Kettapun, A.; Kananthai, A.; S. Suantai A new approximation method for common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, Comp. Appl. Math., Volume 60 (2010), pp. 1430-1439

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