Mixed Variational Inequality Problem Involving Generalized Yosida Approximation Operator in q-Uniformly Smooth Banach Space

A mixed variational inequality problem involving generalized Yosida approximation operator is considered and studied in q-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.

Automated summary

We investigate a mixed variational inequality problem involving the generalized Yosida approximation operator in q-uniformly smooth Banach space and establish its equivalence to a fixed-point equation. Based on this formulation, we propose an algorithm to solve the problem and discuss convergence criteria. We provide an example with Matlab program, computation table, and convergence graphs to verify the effectiveness of the problem and its fixed-point formulation.