Abstract

The purpose of the present work is to introduce a generalized graphic θ-contraction conditions on a family of mappings defined on subsets of a metric space endowed with a set-transitive directed graph, and discuss common fixed point results without considering any kind of commutativity and continuity of the family of mappings. Useful examples illustrate the applicability and effectiveness of the given notions and results. We apply our result to the problem of existence of solutions of a pair of mixed Volterra-Fredholm integral inclusion equations followed by a numerical example.

中文翻译：

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有向图上的多值广义图形 θ-收缩及其在混合 Volterra-Fredholm 积分包含方程中的应用

摘要

本工作的目的是在具有集合传递有向图的度量空间子集上定义的一系列映射上引入广义图形θ -收缩条件，并讨论常见的不动点结果，而不考虑任何类型的交换性和映射族的连续性。有用的例子说明了给定概念和结果的适用性和有效性。我们将我们的结果应用于一对混合 Volterra-Fredholm 积分包含方程的解的存在性问题，然后是一个数值示例。