In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.

In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has been recommended and solved by employing an iterative algorithm. We establish the equivalence between nonlinear fuzzy ordered variational inclusion problem and nonlinear fuzzy ordered resolvent equation problem. The existence and convergence analysis of the solution of nonlinear fuzzy ordered variational inclusion problem involving XOR operation has been substantiated by applying a new resolvent operator method with XOR operation technique. The iterative algorithm and results demonstrated in this article have witnessed a significant improvement in many previously known results of this domain.

This paper examines $\mathcal{H}(·,·)$-accretive mappings in Banach spaces and proves that the resolvent operator related to these mappings is Lipschitz continuous. Using the resolvent operator technique, we formulate iterative algorithms to solve a class of variational inclusions in Banach spaces. We also concentrate on examining the convergence of the problem by employing the inertial extrapolation scheme and proving the convergence of the iterative scheme produced by the algorithm. The theoretical analysis is corroborated with a numerical result, which highlights the effectiveness and practical relevance of the proposed approaches.

In this paper we consider the completely generalized multi-valued co-variational inequality problem in Banach spaces and construct an iterative algorithm. We prove the existence of solutions for our problem involving strongly accretive operators and convergence of iterative sequences generated by the algorithm.