Banach空间中一类非线性算子方程解的存在性

Existence of the Solution for a Class of Nonlinear Operator Eqations in Banach

证明了Banach空间X中闭凸集D上的弱内向、非扩展映射T的平移不变性,并证明了当(I-T)(D)为闭集时T有不动点,进而针对李普希兹映射T给出了Tx=λx型方程解的存在性定理.这些结论推广并改进了某些重要结论.

This paper first proves the translation invarint property of weakly inward and nonexpensive on closed convex set in Banach space. Then, the fixed point theorem for T is established. At the same time, the existence theorem of the solution for equation Tx = Ax is obtained where T is Lipschitz map. Some of the results generalize and improve some important arguments in [3] and [4].