Nonexpansive , Monnotone, Acretive and Cyclic Operators: Applications

PI (subproject 1): Genaro López Acedo

PI (subproject 2): Jesús García Falset

Abstract: In this Project, different classes of linear and nonlinear operators are studied at the time that connections among several branches of Mathematical Analysis such as Geometry of Banach and Metric Spaces, Metric and Topological Fixed Point Theory, Optimization, Cyclic Operators and Linearity are also pursued. Our main goal is to study the relationship between the geometric properties of the linear space (or manifold) where the operators under consideration are defined and the existence and approximation of solutions of functional equations in this space. Furthermore, we intend to study the existence of cyclic, hypercyclic or frequently hypercyclic vectors with respect to sequences of operators defined on spaces of analytic functions. Especially, the algebraic and topological structure of the family of these vectors, as well as the lineability of nonlinear subsets in topological vector spaces, will be investigated.  

 Although this Project corresponds to Fundamental Mathematic, its results find applications in different areas of Mathematics such as Differential and Integral Equations, Approximation Theory, Game Theory, and even in more interdisciplinary fields as Image Recovery, Tomography, Chaos Theory, etc.