Abstract
In this paper, we introduce a new class of variational inclusions involving three operators. We suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique. We also study the convergence criteria of three-step iterative method under some mild conditions. Inertial type methods are suggested and investigated for general variational inclusions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results.
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