Existence And Stability Of Solutions Of Iterative Integral Inclusions

Iterative functional equations is of great significance in both mathematical theoryand practical application, and the researches on iteration have been kept on.The existence and stability of the solutions of a class of series-like iterative integralinclusions with a set-valued mapping and a functional is discussed in this thesis bymeans of the theories and methods about set-valued mappings.The main content of thisdissertation consists of three parts as follows.1. One kind of generalization of the Krasnoselskii’s fixed-point theorem andFan-Kakutani fixed-point theorem are established. The link between thehomeomorphism, set-valued mappings and contraction mappings is considered in thepaper. And on this basis, the sufficient existence conditions of the solutions of a classof operator inclusions with a set-valued mapping are obtained by virtue of fixed pointmethod.2. This paper studies the existence of the solutions of a class of series-like iterativeintegral inclusions with a set-valued mapping and a functional. Firstly, the interrelatedproperties of the series-like iterative functions induced by the Lipschitz functions arediscussed. Secondly, on the basis of the conditions for the existence of the solutions of aclass of operator inclusions with a set-valued mapping, the existence of continuoussolutions on a local finite interval is proved. Thirdly, by extending the solutions from alocal finite interval to the whole closed interval, we obtain the conditions for theexistence of continuous solutions of the iterative integral inclusions which areconsidered by this thesis on an arbitrary closed interval and meanwhile the conditionsimply the boundedness of the solutions.3. We study the stability of a class of iterative systems with a set-valued mappingand a functional. It is proved that the iterative systems Lyapunov stability can bemaintained under certain conditions. At last, the stability of the solutions of iterativeintegral inclusions is explored, and the conditions for stability are obtained.