The purpose of this paper is to introduce a new H(·, ·)‐cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with H(·, ·)‐cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.

In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem ($S_p$VIP) in Hilbert space. We discuss the weak convergence for ($S_p$VIP) and strong convergence for the common solution of ($S_p$VIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes.

This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.

This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.