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We prove a general form of a fixed point theorem for mappings from a Riemannian manifold into itself which are obtained as perturbations of a given mapping by means of general operations which in particular include the cases of sum (when a Lie g[...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2003-07-01We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even [...]texto impreso
In this paper we find an alternative description of the Bochnak complexification of a real Hilbert space. This new interpretation of the Bochnak norm lets us give a characterization of a real inner product space.texto impreso
In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases[...]texto impreso
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The authors show that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}. The key is to show this for a closed halfspace. This result has several attractive consequen[...]texto impreso
In this paper we establish several results which allow to find fixed points and zeros of set-valued mappings on Riemannian manifolds. In order to prove these results we make use of subdifferential calculus. We also give some useful applications.texto impreso
We show how an operation of inf-convolution can be used to approximate convex functions with $C^1$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other pr[...]texto impreso
The notion of Kuratowski convergence is applied to describe a kind of convergence in the context of holomorphic functions. We associate it to a convenient topology, explore its relation with the compact-open topology, thus providing a new set th[...]texto impreso
Let f : R(2) --> R be an open polynomial function. Then, f changes sign across V(f) (alternatively around a singular point of V(f)) and the function c : R --> N expressing the number c(lambda) of connected components of the lambda-level curve [...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2006-11-01We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form u(t) + F(t, d(x)u) = 0, u(0, x) = u(0)(x), where u(0): M -> R is a bounded uniformly continuous function, M is a Riemannian manifold, and F:[...]texto impreso
In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. F[...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2005-03-15We establish some perturbed minimization principles, and we develop a theory of subdifferential calculus, for functions defined on Riemannian manifolds. Then we apply these results to show existence and uniqueness of viscosity solutions to Hamil[...]texto impreso
We prove that every function f:Rn?R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n?1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof,[...]texto impreso
We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Frechet differentiable: We also characterize the Gateaux differentiability of the norm. Finally we stu[...]
