| Summary: | Perturb Extended GQVI provide natural, unified, simple and novel context to study an extensive class of equilibrium problems arising in various fields. In this work, we familiarize and study a number of new and known computational approaches to solve new class of QVI with three nonlinear machinists ${T_\varepsilon }, g \textrm{and} h $ by using different techniques including auxiliary approach and projection approach. We also deal with the existence of the solution of this newly established class of VI, as well as discuss the convergent theorem of the new algorithm by using the projection principal approach, which is simple as compared with other known classes of VI. Our consequences present an important enhancement of earlier recognized techniques for explaining various classes of VI. We are also debating several similar techniques as special cases. Several real-life equilibrium undeveloped problems have been proposed for further open new exploration horizon.
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