On the space of continuous functions from a line segment to a reflexive Banach space, we consider some operator whose values are closed convex subsets of the space. If the values are singletons, the operator becomes a well-known single-valued history-dependent operator. We study the properties of the operator, prove a fixed-point theorem analogous to the fixed-point theorem for single-valued history-dependent operators, and provide some examples. The results are applied to study implicit (unresolved for derivatives) evolution inclusions with maximal monotone operators and with perturbations in a Hilbert space. These perturbations are single-valued and multivalued history-dependent operators.

在从线段到自反Banach空间的连续函数的空间上，我们考虑一些算子，其值是该空间的闭合凸子集。如果值是单例，则运算符将成为众所周知的单值历史依赖运算符。我们研究了算子的性质，证明了一个类似于单值历史相关算子的不动点定理的不动点定理，并提供了一些例子。结果用于研究具有最大单调算子和希尔伯特空间中的扰动的隐式（导数未解析）演化包含。这些扰动是单值和多值历史相关运算符。