Abstract
This paper is dedicated to the introduction a new class of equilibrium problems named generalized multivalued equilibrium-like problems which includes the classes of hemiequilibrium problems, equilibrium-like problems, equilibrium problems, hemivariational inequalities, and variational inequalities as special cases. By utilizing the auxiliary principle technique, some new predictor-corrector iterative algorithms for solving them are suggested and analyzed. The convergence analysis of the proposed iterative methods requires either partially relaxed monotonicity or jointly pseudomonotonicity of the bifunctions involved in generalized multivalued equilibrium-like problem. Results obtained in this paper include several new and known results as special cases.
Highlights
During the last decades, the theory of variational analysis including variational inequalities (VI) have attracted a lot of attention because of its applications in optimization, nonlinear analysis, game theory, economics, and so forth; see, for example, [ ] and the references therein
By replacing the linear term appearing in the formulation of variational inequalities by a vector-valued term, Parida et al [ ] and Yang and Chen [ ] independently introduced and studied a class of variational inequalities known as variational-like inequalities or pre-variational inequalities which is an important extension of the variational inequalities
Another useful and important generalization of variational inequalities is a class of variational inequalities known as hemivariational inequalities involving the nonlinear Lipschitz continuous functions
Summary
The theory of variational analysis including variational inequalities (VI) have attracted a lot of attention because of its applications in optimization, nonlinear analysis, game theory, economics, and so forth; see, for example, [ ] and the references therein. Taking into consideration the fact that the multivalued operators S and T are M-Lipschitz continuous with constants σ and δ, respectively, in virtue of the inequalities Taking into account of the fact that the multivalued operator S is M-Lipschitz continuous with constant σ , in a similar way to that of proof of
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