Abstract
We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space.
Highlights
Let E be a real Banach space and let E∗ be the dual space of E
It is well known that the variational inequalities are equivalent to the fixed point problems
There are many authors who studied the problem of finding a common element of the fixed point of nonlinear mappings and the set of solutions of a variational inequality in the framework of Hilbert spaces see; for instance, 1–11 and the reference therein
Summary
Let E be a real Banach space and let E∗ be the dual space of E. Inoue et al 20 proved the following strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a relatively nonexpansive mapping by using the hybrid method.
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