# Modified Halpern-type iterative methods for relatively nonexpansive mappings and maximal monotone operators in Banach spaces

@inproceedings{Wu2014ModifiedHI, title={Modified Halpern-type iterative methods for relatively nonexpansive mappings and maximal monotone operators in Banach spaces}, author={Huan-chun Wu and Cao-zong Cheng}, year={2014} }

- Published 2014
DOI:10.1186/1687-1812-2014-237

We obtain the modified Halpern-type iterative method for finding a common element of the fixed point set of a relatively nonexpansive mapping and the zero set of a maximal monotone operator in a uniformly convex and uniformly smooth Banach space. Our results extend and improve the recent results of Chuang, Lin and Takahashi (J. Glob. Optim. 56:1591-1601, 2013) and Nilsrakoo and Saejung (Appl. Math. Comput. 217:6577-6586, 2011). MSC: 47H05; 47H09; 47J25