局部凸空间中凸幂凝聚算子的不动点定理及其应用
The Fixed Point Theorem of Convex-Power Condensing Operator and Its Applications in Locally Convex Spaces
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摘要: 首先给出了局部凸空间中一类新的算子--凸幂凝聚算子的定义,推广了Banach中的凝聚算子,并获得了这类凸幂凝聚算子的一个不动点定理.作为应用,本文建立了一类半线性发展方程的解的存在性结果.Abstract: In this paper, the definition of a kind of new operator, i. e. , convex-power condensing operator in locally convex spaces, is given, which generalizes the definition of condensing operator in Banach space. Then a new fixed point theorem of this kind of new operator is obtained. As applications, we establish a criterion for mild solutions to initial value problems of a class of abstract semilinear evolution equations in locally convex spaces.
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