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

AbstractWe 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.

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