Topological Transversality Coincidence Theory for Multivalued Maps with Selections in a Given Class

This paper presents the topological transversality coincidence theorem for general multivalued maps who have selections in a given class of maps.

Complete periodic adaptive antisynchronization of memristor-based neural networks with mixed time-varying delays

This paper is concerned with the complete periodic antisynchronization issue of memristor-based neural networks with mixed time-varying delays. Under the framework of Filippov solutions of the differential equations with discontinuous right-hand side, based on Mawhin-like coincidence theorem in set-valued analysis theory, the proof of the existence of periodic solution is presented. By applying the Lyapunov–Krasovskii functional approach, adaptive controller is designed and unknown control parameters of the slave system are determined by adaptive laws, and the complete periodic adaptive antisynchronization condition is addressed to ensure the slave system global antisynchronization with the master system. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Some KKM theorems in modular function spaces

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

Ky Fan Matching Theorems for MFC Mappings in FC-Metric Spaces with the Application to Minimax Inequalities

In this paper, MFC mappings is introduced and Ky Fan matching theorems for MFC mappings with transfer compactly open values are established in noncompact complete FC-metric spaces. As applications, a Fan-Browder type coincidence theorem and a minimax inequality are obtained. Our results unify, improve and generalize some known results in recent literature.

Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by usingM-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.