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To consider existence of solutions to various optimization-related problems, we first develop some equivalent versions of invariant-point theorems. Next, they are employed to derive sufficient conditions for the solution existence for two general models of variational relation and inclusion...
Persistent link: https://www.econbiz.de/10010896442
We consider a general equilibrium problem under weak coercivity conditions in a finite-dimensional space setting. It appears such a condition provides convergence of the general penalty method without any monotonicity assumptions. We also show that the regularized version of the penalty method...
Persistent link: https://www.econbiz.de/10010845813
We consider various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. By using first and second-order approximations as generalized derivatives, we establish both necessary and sufficient optimality conditions. Our first-order conditions are shown to be...
Persistent link: https://www.econbiz.de/10010845851
Our purpose in this paper is to prove strong convergence theorem for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup and the set of solutions to a system of equilibrium problems in a real Hilbert space using a new iterative method. Finally, we...
Persistent link: https://www.econbiz.de/10010845867
We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using...
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