Fixed point problems and iterations of monotone mappings

The goal of this project is to study: (1) the existence of fixed points (2) explicit iteration processes for monotone mappings defined on certain nonlinear domains in Banach, hyperbolic metric spaces, or modular spaces endowed with a partial order or a graph. In particular, weak- convergence and strong convergence of these iteration processes will be investigated. We will also investigate the existence of common fixed points of such mappings. We anticipate that our results will contain some well-known results in Hilbert spaces and uniformly convex Banach spaces as a special case - thus broadening the scope of existing iterative approximation theory of fixed points on nonlinear domains to the case of monotone mappings.