title: Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities.
abstract: The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities.
authors.affiliation: Department of Mathematics, Tianjin University, Tianjin, 300350 China.
authors.forename: Jingling
authors.initials: J
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, Tianjin University, Tianjin, 300350 China.
authors.forename: Nan
authors.initials: N
authors.lastname: Jiang
keywords: Fixed point; Inverse-strongly monotone mapping; Maximal monotone operator; Quasi-nonexpansive mappings