Search results for "Nonlinear operators"
showing 7 items of 7 documents
Existence of fixed points and measures of weak noncompactness
2009
Abstract The purpose of this paper is to study the existence of fixed points by using measures of weak noncompactness. Later on, we provide an existence principle for solutions for a nonlinear integral equation.
The fixed point property for mappings admitting a center
2007
Abstract We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
2020
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solut…
Existence results for a nonlinear nonautonomous transmission problem via domain perturbation
2021
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.
An extension of Guo's theorem via k--contractive retractions
2006
Abstract Let X be a infinite-dimensional Banach space. We generalize Guo's Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k- ψ -contractions and condensing mappings, under a condition which depends on the infimum k ψ of all k ⩾ 1 for which there exists a k- ψ -contractive retraction of the closed unit ball of the space X onto its boundary.
On the use of generalized harmonic means in image processing using multiresolution algorithms
2019
In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new famil...