We study sufficient conditions for existence of solutions to the global optimization problem $min_{xin A}d(x,fx),$ where $A,$ $B$ are nonempty subsets of a metric space $(X,d)$ and $f:Ao B$ belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
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机译：我们研究全局优化问题$ min_ {x in A} d（x，fx），$的解存在的充分条件，其中$ A，$ $ B $是度量空间$（X，d ）$和$ f：A 至B $属于近端模拟收缩映射的一类。我们的结果统一，改进和归纳了有关该主题的现有文献中的各种可比结果。作为所得定理的一个应用，我们给出了变分不等式问题的一些可解性定理。
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