Xue Xiaoping

Random fuzzy number integrals in Banach spaces

Abstract In this paper, a new kind of random fuzzy number integral is introduced by the Pettis-Aumann integral of the set-valued functions in Banach spaces. The existence of the random fuzzy integral is also shown. Levis convergence theorem of the integral is given a special mention.

On the extension of the fuzzy number measures in Banach spaces: Part I. Representation of the fuzzy number measures

Abstract In this paper, the definition of the fuzzy number measures which extends the concepts of the set-valued measures in Banach spaces is introduced. The relations between the fuzzy number measures and the set-valued measures are studied. The definition of the indefinite integral of the random fuzzy numbers is also introduced and its properties are discussed.

On the null-additivity of the fuzzy measure

Abstract In this paper, Egoroffs theorem and other several results on fuzzy measure space of papers [1] and [4] are improved. The importance of the concept of null-additivity, which was first introduced by Wang in [1], is further shown.

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces.

EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p ( t )-LAPLACIAN

We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi-linear differential inclusion. Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi-linear differential inclution. An application to some feedback control systems is discussed.

On stability of delayed cellular neural networks with sigmoid output functions

In this paper a sufficient condition is presented to ensure the complete stability of delayed CNNs. Such a condition establishes a relation between the time delay and the parameters of the networks. Specially, for a given output function f(x) = tanh(x), we address a sufficient condition to ensure absolute convergence of system state.