中文摘要：

给出广义凝聚算子和广义凸幂凝聚算子的概念,并证明这类新算子的最小和最大不动点的存在性。作为应用,研究了Banach空间中一类半线性发展方程初值问题的最小最大mild解的存在性。

英文摘要：

The concepts of generalized condesion operator and generalized convex power condesion operator are introduced,and the existence of the maximal and minimal fixed point of this kind of new operator is proved.As an application,the existence of the maximal and minimal mild solution of the initial problem for a class of semilinear evolution equation is obtained in Banach space.