Abstract
In this paper, a new system of generalized nonlinear variational inequalities involving three operators is introduced. A three-step iterative algorithm is considered for the system of generalized nonlinear variational inequalities. Strong convergence theorems of the three-step iterative algorithm are established.MSC:47H05, 47H09, 47J25.
Highlights
Variational inequalities are among the most interesting and intensively studied classes of mathematical problems and have wide applications in the fields of optimization and control, economics, transportation equilibrium and engineering sciences
There exists a vast amount of literature on the approximation solvability of nonlinear variational inequalities as well as operator equations
Iterative algorithms have played a central role in the approximation solvability, especially of nonlinear variational inequalities as well as of nonlinear equations, in several fields such as applied mathematics, mathematical programming, mathematical finance, control theory and optimization, engineering sciences and others
Summary
Variational inequalities are among the most interesting and intensively studied classes of mathematical problems and have wide applications in the fields of optimization and control, economics, transportation equilibrium and engineering sciences. Chang et al [ ] introduced a two-step iterative algorithm for a system of nonlinear variational inequalities and established strong convergence theorems.
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