Fixed Point Theorems And Application Based On The Measure Of Noncompactness

Two operators are researched in this paper,one of them is Monch type map,the other is Meir-Keeler condensing operator.At first,We respectively discuss the M(?)nch type map in two domains.1.The cases without bounded assumption on domain.Firstly,we prove the existence of fixed point for Monch type map respectively under Rothe and Altman conditions.And then we obtain the extension theorem.In addition,a result of a priori estimate is given for Monch type map.2.The case with strictly star-shaped bounded domain.The existence of fixed point is obtained in this part for M(?)nch type map respectively under the condition of Schauder type and interior conditions of Leray-Schauder,Rothe and Altman types.Besides,we prove the extension theorem of M(?)nch type map with strictly star-shaped with respect to x0 bounded domain.Next,we study the Meir-Keeler condensing operator.As the generalization of self-mapping Meir-Keeler condensing operator,a fixed point theorem of nonself-mapping Meir-Keeler condensing operator is given under the condition of Leray-Schauder.And on this basis we prove the fixed point theorems respectively under conditions of Rothe and Altman types.Furthermore a priori estimate theorem is obtained with application to the existence of solutions for an integral equation of Volterra type.