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| Paper IPM / M / 17361 |
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| Abstract: | |
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In this paper, we extend the definition of the qx-asymptotic functions, for an extended realvalued function defined on the infinite-dimensional topological normed spaces without lower
semicontinuity or quasi-convexity condition. As the main result, by using some asymptotic
conditions, we obtain sufficient optimality conditions for the existence of solutions to equilibrium problems, under weaker assumptions of continuity and convexity, when the feasible
set is an unbounded subset of infinite-dimensional space. Also, as a corollary, we obtain
necessary and sufficient optimality conditions for the existence of solutions to equilibrium
problems with an unbounded feasible set. Finally, as an application, we establish a result for
the existence of solutions to minimization problems.
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