Papers by José María Soriano Arbizu
Extracta Mathematicae, 1991
arXiv: Functional Analysis, 2020
Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X... more Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X, where F is a C^1-operator, and C a C^1 compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a C^1-diffeomorphism. Three corollaries are given. The first one, when F is a linear homeomorphism. The second one, when F is a k-contractive perturbation of the identity. The third one, when X is a Hilbert space and F a particular linear operator. The proof of our results is based on properties of Fredholm operators, as well as on local and global inverse mapping theorems, and the Banach fixed point theorem. As an application two examples are given
Acta Mathematica Scientia, 2002
A sufficient condition is given to assert that a continuous mapping between R'" and R" has a zero... more A sufficient condition is given to assert that a continuous mapping between R'" and R" has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.
Journal of the Korean Mathematical Society, 2009
Journal of the Korean Mathematical Society, 2008
Czechoslovak Mathematical Journal, 2011
Some sufficient conditions are provided that guarantee that the difference of a compact mapping a... more Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over K has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method.
Bulletin of the Brazilian Mathematical Society, New Series, 2007
Sufficient conditions are given to assert that a perturbed mapping has a zero in a Banach manifol... more Sufficient conditions are given to assert that a perturbed mapping has a zero in a Banach manifold modelled over R n. The zero is estimated by means of sequences of Newton's iterations. The proof of the result is constructive and is based upon continuation methods.
Applied Mathematics and Mechanics, 2005
The stability of stationary trajectories of a particular autonomous system is studied. The proof ... more The stability of stationary trajectories of a particular autonomous system is studied. The proof of the result is based upon continuation methods.
Applied Mathematics and Mechanics, 2001
Sufficient conditioJ~,~ are given to assert that two differentiable mappings between Banach space... more Sufficient conditioJ~,~ are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
Applied Mathematics and Computation, 2001
Sucient conditions are given to assert that a dierentiable mapping between K m and K n , where K ... more Sucient conditions are given to assert that a dierentiable mapping between K m and K n , where K R or K C, has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.
Applied Mathematics and Computation, 1997
as can clearly be seen in the proof. As is obvious, all the components of the construct homotopy ... more as can clearly be seen in the proof. As is obvious, all the components of the construct homotopy must be in a compact. We regret any inconvenience.
Applied Mathematics and Computation, 1997
We prove the existence of the exact number of zeros of a mapping under smoothness conditions. The... more We prove the existence of the exact number of zeros of a mapping under smoothness conditions. The proof is constructive: numerical methods can be used to follow a solution curve with a computer. Weakening the conditions, we have the existence of at least one zero.
Applied Mathematics and Computation, 2001
It is proven that an initial value problem of an autonomous system verifying some conditions has ... more It is proven that an initial value problem of an autonomous system verifying some conditions has exactly one open continuously dierentiable trajectory on R, whose limit set is not one point. The proof of the result is based upon continuation methods.
Applied Mathematics and Computation, 1993
In this paper we prove the existence of an unique global minimum point of a convex function under... more In this paper we prove the existence of an unique global minimum point of a convex function under some smoothness conditions. Our proof permits us to calculate numerically such a minimum point utilizing a constructive homotopy method.
Applied Mathematics and Computation, 2006
Sufficient conditions are given to assert that a perturbed mapping has only one zero in a specifi... more Sufficient conditions are given to assert that a perturbed mapping has only one zero in a specific open ball. This zero is estimated by means of a sequence of NewtonÕs iterations. The proof of the result is constructive and is based upon continuation methods.
Applied Mathematics and Computation, 1999
Sufficient conditions, asserting the existence of at least one zero of bounded perturbations of p... more Sufficient conditions, asserting the existence of at least one zero of bounded perturbations of proper mappings, are given. The conditions are easily tested. The proof of this theorem is constructive, showing the existence of a solution curve that can be followed by numerical methods.
Acta Mathematica Scientia, 2010
Sufficient conditions are given to assert that two C 1-mappings share only one value in a connect... more Sufficient conditions are given to assert that two C 1-mappings share only one value in a connected compact Banach manifold modelled over R n. The proof of the result, which is based upon continuation methods, is constructive.
Acta Mathematica Scientia, 2007
It is proven that an autonomous system verifying some conditions has at least one stable stationa... more It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectories.
In this paper we prove the existence of an unique global minimum point of a convex function under... more In this paper we prove the existence of an unique global minimum point of a convex function under some smoothness conditions. Our proof permits us to calculate numerically such a minimum point utilizing a constructive homotopy method.
For a map / of class two a sufficient condition is obtained to secure the existence of a zero of ... more For a map / of class two a sufficient condition is obtained to secure the existence of a zero of / in the simplex 5 if a piecewise Hnear aproximation 9 of f has a cero in s. AppHcation: for a smooth map F: Z) Ê C" > C a noniterative algorithm is constructed of obtain the zeros of F using the usual homotopy H in Dx [0, 1] and a piecewise Hnear approximation 6 relative to a triangulation K of Dx [0, 1]. An implemention of the procedure is cited. Resumen Para una apHcación / de clase dos se obtiene una condición suficiente para asegurar la existencia de un cero de / en el simplex s si una aproximación Hneal a trozos 6 de f tiene un cero en s. ApHcación: para una apHcación regular F: D & C^ > C" se construye un algo 1 ritmo no iterativo para calcular sus ceros, utilizando la homotopía usual H en D x [O, 1] y una aproximación Hneal a trozos 6 relativa a una triangulación K ÚQ Dx [O, 1]. Se cita una aplicación del procedimiento.
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Papers by José María Soriano Arbizu