A Study of Solutions of Variational Inequality, System and Mixed Equilibrium Problem

The equilibrium problem incorporates numerous mathematical problems as specific cases for cases, scientific programming problems, complementary problems, variational disparity problems, and saddle point problems, Nash equilibrium problems in non-cooperative games, mini-max imbalance problems, minimization problems and fixed point problems.As of late, much consideration has been given for creating efficient and implementable iterative methods including projection method and its variation frames, extra-gradient method, linear approximation, auxiliary principle method, descent and Newton methods for VIPs and EPs.Then again, numerous issues emerging in different zones of mathematics, for example, optimization, variational analysis and differential equations, can be demonstrated by fixed point issue (FPP) comprising of discovering x ∈C to such an extent that x = Tx, where T is a nonlinear self-guide on C. Fix(T ) signifies the arrangement of fixed purposes of T . The investigation of iterative strategies, viz. Helpern iterative strategy, Mann and Ishikawa iterative strategies, and consistency estimate technique for FPP has yielded a large group of works in the most recent decades.There is a substantial number of iterative strategies for concentrate independently, the fixed point issues for nonlinear mappings, variational inequalities, and equilibrium issues. It is of further enthusiasm to create and ponder the iterative techniques to estimate the common arrangements of these issues.