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Covering mappings and their applications in functional equations, difference equations and optimization (COVMAPS)
Date du début: 1 juil. 2014, Date de fin: 30 juin 2015 PROJET  TERMINÉ 

There will be considered covering mappings and their applications. The properties of covering mappings in generalized metric spaces will be studied. Moreover, sufficient solvability conditions for inclusions defined by conditionally covering multi-valued mappings in metric spaces will be obtained. This results will be applied to the following problems. For difference equations there will be studied such issues as solvability, equilibrium existence and stability. In addition, there will be studiedseveral types of functional equations. This part of research will be based on the result obtained for covering mappings in generalized metric spaces. Finally, there will be studied questions of global solvability for control systems and necessary optimality conditions for control systems defined by Volterra equations.