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The research program of the COVMAPS program concerns covering mappings and their applications.The key research effort addresses the properties of covering mappings in generalized metric spaces as well as sufficient solvability conditions for multiple types of equations and inclusions defined by conditionally covering multi-valued mappings in metric spaces.
These technical results will be applied to the investigation of solvability conditions, existence of equilibrium, and stability conditions of types of equations and inclusions with practical significance in many application areas. We single out difference equations and several types of functional equations.
The research on the later will be based on results obtained for covering mappings in generalized metric spaces. These results will be the basis to address the technical challenges arising in the research of global solvability conditions for control systems, as well as, necessary optimality conditions for control systems defined by Volterra equations.