Geodesic
Hybrid algorithm for an $\alpha$-nonexpansive mapping in a Banach space
Wang, Zi-Ming1 ; Su, Yongfu2 ; Kang, Jinlong3
1 Department of Foundation, Shandong Yingcai University, Jinan 250104, P. R. China
2 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China
3 Department of Foundation, Xi'an Communication of Institute, Xi'an 710106, P. R. China
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 56-63.

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

In this paper, we prove strong convergence theorem by the hybrid method for an $\alpha$-nonexpansive mapping in a Banach space. Our results complement and enrich the research contents of $\alpha$-nonexpansive mapping. Simultaneously, our main result generalizes Takahashi, Takeuchi, Kubota's result[W. Takahashi, Y. Takeuchi , R. Kubota, J. Math. Anal. Appl. 341 (2008) 276-286].
DOI : 10.22436/jnsa.005.01.07
Classification : 47H05, 47H09, 47H10
Keywords: \(\alpha\)-nonexpansive mapping, \(\alpha\)-mean-asymptotically-nonexpansive mapping, Hybrid algorithm, Fixed point, Banach space.

Wang, Zi-Ming 1 ; Su, Yongfu 2 ; Kang, Jinlong 3

1 Department of Foundation, Shandong Yingcai University, Jinan 250104, P. R. China
2 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China
3 Department of Foundation, Xi'an Communication of Institute, Xi'an 710106, P. R. China 
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Wang, Zi-Ming; Su, Yongfu; Kang, Jinlong. Hybrid algorithm for an  \(\alpha\)-nonexpansive mapping in a Banach space. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 56-63. doi : 10.22436/jnsa.005.01.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.01.07/

[1] C. Chidume Geometric properties of Banach spaces and nonlinear iterations, vol. 1965 of Lecture Notes in Mathematics, Springer, London, UK, 2009

[2] Wittmann, R. Approximation of fixed points of nonexpansive mappings, Arch. Math., Volume 58 (1992), pp. 486-491

[3] Berinde, V. Iterative Approximation of Fixed Points, vol. 1912 of Lecture Notes in Mathematics, Springer, Berlin, 2nd edition, Germany, 2007

[4] Goebel, K.; Pineda, M. A. On a type of generalized nonexpansiveness, Proc. of the 8th International Conference on Fixed Point Theory and its Application, Volume 74 (2007), pp. 660-665

[5] Chakkrid, Klin-eam; Suthep, Suantai Fixed piont theorems for \(\alpha\)-nonexpansive mappings, Applied Mathematics Letters, Volume 23 (2010), pp. 728-731

[6] W. Takahashi Nonlinear Functional Analysis, Fixed Points Theory and its Applications, okohama , Yokohama Publishers, 2000

[7] Cioranescu, I. Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Dordrecht, Kluwer Academic Publishers Group, 1990

[8] Alber, Y. I. Metric and generalized projection operators in Banach spaces: properties and applications, in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Lecture Notes in Pure and Applied Mathematics, New York: Dekker (1996), pp. 15-50

[9] Takahashi, W.; Takeuchi, Y.; R. Kubota Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. , Volume 341 (2008), pp. 276-286

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