Abstract
We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems.
Highlights
Variational inequalities theory, introduced in 1964, has emerged as a powerful tool to investigate and study a wide class of unrelated problems arising in industrial, regional, physical, pure, and applied sciences in a unified and general framework
We consider a new class of equilibrium problems, known as hemiequilibrium problems
Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity
Summary
We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. We obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems
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