Análisis Matemático
https://hdl.handle.net/11441/10808
2019-05-19T16:59:23ZHausdorff and Box dimensions of continuous functions and lineability
https://hdl.handle.net/11441/86325
Hausdorff and Box dimensions of continuous functions and lineability
Given s ∈ (1, 2], we study (among other questions) the algebraic genericity of the set of continuous functions f : [0, 1] → R whose graph has Hausdorff (or Box) dimension exactly s.
2019-05-01T00:00:00ZSubspaces of frequently hypercyclic functions for sequences of composition operators.
https://hdl.handle.net/11441/85392
Subspaces of frequently hypercyclic functions for sequences of composition operators.
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such a criterion improves some already known special cases, and, in addition, it is also valid to provide dense vector subspaces as well as large closed ones consisting entirely, except for zero, of functions that are frequently hypercyclic.
2019-02-01T00:00:00ZEquilibrium problems on Riemannian manifolds with applications
https://hdl.handle.net/11441/83899
Equilibrium problems on Riemannian manifolds with applications
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent
for the equilibrium problem on Hadamard manifolds.
2019-05-15T00:00:00ZRate of convergence under weakcontractiveness conditions
https://hdl.handle.net/11441/83468
Rate of convergence under weakcontractiveness conditions
We introduce a new class of selfmaps T of metric spaces, which generalizes the
weakly Zamfirescu maps (and therefore weakly contraction maps, weakly Kannan maps,
weakly Chatterjea maps and quasi-contraction maps with constant h < 1
2
). We give an
explicit Cauchy rate for the Picard iteration sequences {T
nx0}n∈N for this type of maps,
and show that if the space is complete, then all Picard iteration sequences converge to the
unique fixed point of T. Our Cauchy rate depends on the space (X, d), the map T, and the
starting point x0 ∈ X only through an upper bound b ≥ d(x0, T x0) and certain moduli θ, µ
for the map, but is otherwise fully uniform. As a step on the way to proving our fixed point
result we also calculate a modulus of uniqueness for this type of maps.
2013-01-01T00:00:00Z