In this paper, we first introduce the concept of graphical convex metric spaces and some basic properties of the underlying spaces. Different from related literature, we generalize Mann iterative scheme and Agrawal iterative scheme for set-valued mappings to above spaces by introducing the concepts of T-Mann sequences and T-Agrawal sequences. Furthermore, by using the iterative techniques and graph theory, we investigate the existence and uniqueness of fixed points for set-valued G-contractions in a graphical convex metric space. Moreover, we present some notions of well-posedness and G-Mann stability of the fixed point problems in the above space. Additionally, as an application of our main results, we discuss the well-posedness and G-Mann stability of the fixed point problems for set-valued G-contractions in a graphical convex metric space.

在本文中，我们首先介绍图形凸度量空间的概念以及底层空间的一些基本属性。与相关文献不同，我们通过引入T -Mann序列和T -Agrawal序列的概念，将Mann迭代方案和Agrawal迭代方案推广到上述空间的集值映射。此外，通过使用迭代技术和图论，我们研究了图形凸度量空间中集值G压缩不动点的存在性和唯一性。此外，我们提出了适定性和G的一些概念-上述空间中定点问题的人为稳定性。另外，作为我们主要结果的应用，我们讨论了图形凸度量空间中集值G-压缩不动点问题的适定性和G -Mann稳定性。