In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.

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 ...

The Multi-scale Variance Stabilization Transform (MSVST) has recently been proposed for 2D Poisson data denoising. In this work, we present an extension of the MSVST with the wavelet transform to multivariate data–each pixel is vector-valued–, where the vector field dimension may be the wavelength, the energy, or the time. Such data can be viewed naively as 3D data where the third dimension may...

Article history: Received 19 February 2009 Received in revised form 28 October 2011 Accepted 21 December 2011 Available online 23 December 2011

Bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Given by a graph M representing a multivalued constitutive law, we state a simple necessary and sufficient condition for the existence of a bipotential b for which M is the set of (x, y) such tha...