Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Biologically-inspired data decorrelation for hyper-spectral imaging

Hyper-spectral data allows the construction of more robust statistical models to sample the material properties than the standard tri-chromatic color representation. However, because of the large dimensionality and complexity of the hyper-spectral data, the extraction of robust features (image descriptors) is not a trivial issue. Thus, to facilitate efficient feature extraction, decorrelation techniques are commonly applied to reduce the dimensionality of the hyper-spectral data with the aim of generating compact and highly discriminative image descriptors. Current methodologies for data decorrelation such as principal component analysis (PCA), linear discriminant analysis (LDA), wavelet decomposition (WD), or band selection methods require complex and subjective training procedures and in addition the compressed spectral information is not directly related to the physical (spectral) characteristics associated with the analyzed materials. The major objective of this article is to introduce and evaluate a new data decorrelation methodology using an approach that closely emulates the human vision. The proposed data decorrelation scheme has been employed to optimally minimize the amount of redundant information contained in the highly correlated hyper-spectral bands and has been comprehensively evaluated in the context of non-ferrous material classification

Caprate: un sistema de interpretación de problemas en lenguaje natural

199 p.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.