The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

In this paper, based on the viscosity approximation method and the hybrid steepest-descent iterative method, a new implicit iterative algorithm is presented for finding the common fixed points set of a finite family of nonexpansive mappings in a reflexive Hilbert space, which is called a symmetric space. We prove that the sequence generated by this new implicit rule strongly converges to the unique solution of a class of variational inequalities under certain appropriate conditions of the parameters. Moreover, we also study the applications to a broader family of strictly pseudo-contractive mappings and generalized equilibrium problems that involve several variational inequality problems, optimization problems, and fixed-point problems. Finally, numerical results are provided to clarify the stability and effectiveness of the algorithm and to compare with some existing iterative algorithms.

This paper is devoted to introducing a new implicit iterative algorithm based on viscosity approximation method and hybrid steepest-descent iterative method for finding the common fixed points set of a finite family of non-expansive mappings in Hilbert spaces. We certify that the sequences generated by this new implicit rule strongly converges to the unique solution of a class of variational inequalities under some suitable conditions of the parameters. The result extends and improves the corresponding results announced by many others. Moreover, applications to a broader family of λ-strictly pseudo-contractive mappings and generalized equilibrium problems. Finally, numerical results are given to clarify the effectiveness and practicability of the proposed algorithm, which compares with the iterative scheme of Cai and Shehu. Mathematics Subject Classification (2010). 47H10, 47J25, 49J40.

No abstract

No abstract