Geodesic
Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces
Yao, Zhangsong1 ; Zhu, Li-Jun2 ; Liou, Yeong-Cheng3
1 School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China
2 School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China
3 Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan;Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 5, p. 489-495.

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

In this paper, we studied a Halpern-type iteration algorithm involving pseudo-contractive mappings for solving some variational inequality in a q-uniformly smooth Banach space. We show the studied algorithm has strong convergence under some mild conditions. Our result extends and improves many results in the literature.
DOI : 10.22436/jnsa.008.05.04
Classification : 47H05, 47H10, 47H17
Keywords: Halpern iterative algorithm, pseudocontractive mapping, fixed point, variational inequality

Yao, Zhangsong 1 ; Zhu, Li-Jun 2 ; Liou, Yeong-Cheng 3

1 School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China
2 School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China
3 Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan;Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan 
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Yao, Zhangsong; Zhu, Li-Jun; Liou, Yeong-Cheng. Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 5, p. 489-495. doi : 10.22436/jnsa.008.05.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.05.04/

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