Fixed point theorems for set-valued G-contractions in a graphical convex metric space with applications

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.