Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces

Volume 8, Issue 5, pp 489--495 http://dx.doi.org/10.22436/jnsa.008.05.04

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Authors

Zhangsong Yao - School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China. Li-Jun Zhu - School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China. Yeong-Cheng Liou - Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan. - Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan.

Abstract

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.

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Keywords

• Halpern iterative algorithm
• pseudocontractive mapping
• fixed point
• variational inequality

MSC

•  47H05
•  47H10
•  47H17

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