Set-valued contractions of Leader type in quasi-triangular spaces are constructed, conditions guaranteeing the existence of nonempty sets of periodic points, fixed points and endpoints of such contractions are established, convergence of dynamic processes of these contractions are studied, uniqueness properties are derived, and single-valued cases are considered. Investigated dynamic systems are not necessarily continuous and spaces are not necessarily sequentially complete or Hausdorff. Obtained results suggest, in particular, strategies to new studies of functional Bellman equations and variable discounted Bellman equations in metric spaces and integral Volterra equations in locally convex spaces. Results in this direction are also presented in this paper. More precisely, without continuity of Bellman and Volterra appropriate operators, the sets of solutions of these equations (which are periodic points of these operators) are studied and new and general convergence, existence and uniqueness theorems concerning such equations are proved.

中文翻译：

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集值Leader类型的收缩，周期点和端点定理，准三角形空间，Bellman和Volterra方程

构造拟三角空间中Leader型的集值收缩，建立保证非空周期点，定点和端点存在的条件，研究了这些收缩的动态过程，得出了唯一性，并考虑单值情况。研究的动态系统不一定是连续的，空间也不一定是顺序完整的或Hausdorff。获得的结果尤其提出了对度量空间中的函数Bellman方程和可变折价Bellman方程以及局部凸空间中的积分Volterra方程进行新研究的策略。本文还介绍了该方向上的结果。更准确地说，如果没有Bellman和Volterra合适的运算符的连续性，