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.

In this paper, we consider and study a system of generalized variational inclusions involving Cayley operators and an XOR-operation in q-uniformly smooth Banach spaces. To obtain the solution of the system of generalized variational inclusions involving Cayley operators and an XOR-operation, we use some properties of Cayley operators as well as an XOR-operation. We also discuss the convergence criterion. In support of our main result, we provide an example.

In this article, we study a generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation. It is shown that the generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation is equivalent to a fixed point equation. We have proved that the generalized Yosida approximation operator is Lipschitz continuous. Finally, we prove an existence and convergence result for our problem.

In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real Banach space and for the Yosida resolvent equation problem in q-uniformly smooth Banach space. For faster convergence, we apply an inertial extrapolation scheme for both the problems. An example is provided.

A mixed variational inequality problem involving generalized Yosida approximation operator is considered and studied in -uniformly smooth Banach space. We have shown that mixed variational inequality problem involving generalized Yosida approximation operator is equivalent to a fixed-point equation. The fixed-point formulation is applied to establish an algorithm to obtain the solution of mixed variational inequality problem involving generalized Yosida approximation operator. Convergence criteria are also discussed. In support of our main result, we provide an example using Matlab program together with a computation table and convergence graphs. To check the validity of mixed variational inequality problem involving generalized Yosida approximation operator and its fixed-point formulation, we construct one more example.

We focus our study on a co-variational inequality problem involving two generalized Yosida approximation operators in real uniformly smooth Banach space. We show some characteristics of a generalized Yosida approximation operator, which are used in our main proof. We apply the concept of nonexpansive sunny retraction to obtain a solution to our problem. Convergence analysis is also discussed.