This paper extends Krein-Rutman's theorem on linear operators leaving an invariant cone in infinite-dimensional Banach spaces to multivalued convex functions. The result is applied to obtain necessary and sufficient conditions for global controllability and reachability of nonlinear discrete-time systems described by convex processes.

This paper deals with the iteration of algebraic functions, i.e. (in general) multivalued self maps of the Riemann sphere deened by z 7 ! w if P (z; w) = 0, where P is a polynomial in two complex variables. The notion of a hyperbolic repeller is introduced and illustrated by several examples. We prove that hyperbolic repellers are orbit stable under perturbations.

Contents Preface ix 1. Wavelet and frame transforms originated from continuous and discrete splines, Amir Z. Averbuch and Valery A. Zheludev 1 1.1. Introduction 1 1.2. Preliminaries 4 1.3. Prediction filters originated from splines 9 1.4. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 2 (diadic transforms) 17 1.5. Application of spline-based wavelet trans...

In this paper, we introduce some aspects of a critical point theory for multivalued functions Φ : E → RN∪{∞} defined on E a complete gauge space and with closed graph. The existence of a critical point is established in presence of linking. Finally, we present applications of this theory to semilinear elliptic problems on RN .

An important aspect of data modeling is the identification of entities or objects and their associated attributes. An attribute may be single-valued or multivalued. During database design, the designer usually has to represent all attributes in relational tables that only allow single-valued cells. A number of authors (1, 3, 5, 6) advocate the notion that multivalued attributes are essentially ...

We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

Rosenblatt's perceptron is extended to (1) a multivalued perceptron and (2) to a continuous-valued perceptron. It shown that any function that can be represented by the multivalued perceptron can be learned in a nite number of steps, and any function that can represented by the continuous perceptron can be learned with arbitrary accuracy in a nite number of steps. The whole apparatus is deened ...

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results ext...