论文标题
与一个cauchy定理相关的非线性映射的一些通用定理定理
Some general fixed-point theorems for nonlinear mappings connected with one Cauchy theorem
论文作者
论文摘要
在这项工作中，使用一种新的几何方法，我们研究了平稳性独立性及其单价值或多价值的映射的固定点的存在。这项工作证明了在某种意义上概括的定理Brouwer和Schauder固定点定理，并且这种类型在多价值案例中都会导致。可以认为，这种方法是基于一个定理Cauchy的概括和集合的凸性属性。由于使用的方法是基于所检查映射的图像的几何形状，这些映射与空间的拓扑特性无关，我们可以证明几乎每个向量空间的一般结果。我们将一般结果应用于VT中非线性方程和夹杂物的研究，并应用这些结果进行了研究。不同的具体非线性问题。在这里，还提供了足够的条件，在这些条件下，定理的条件将满足。
In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in some sense the Brouwer and Schauder fixed-point theorems, and also such type results in multi-valued cases. One can reckon this approach is based on the generalization of the one theorem Cauchy and on the convexity properties of sets. As the used approach is based on the geometry of the image of the examined mappings that are independent of the topological properties of the space we could to prove the general results for almost every vector space. The general results we applied to the study of the nonlinear equations and inclusions in VTS, and also by applying these results are investigated different concrete nonlinear problems. Here provided also sufficient conditions under which the conditions of the theorems will fulfill.
