An iterative method for common solution to various problems

Abstract

In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for demicontinuous nearly nonexpansive mappings. We prove that our method converges strongly to a common solution of all above problems. It is worth noting that Main Theorem is proved without usual demiclosedness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results. - 2019 Jangjeon Mathematical Society. All rights reserved.