一类k-α-φ随机压缩算子及其不动点

Random Fixed Point for k-α-φ Random Contractive Type Mappings

在完备的度量空间中,应用Banach压缩理论,研究了一类k-α-φ随机压缩型算子及其对应的随机不动点,得到了这类算子有不动点的条件,作为应用,得到了一个非线性泛函随机积分方程的解.

In this paper, we introduce a new concept of k-α-φ -contractive type random mappings and establish fixed point theo-rems for such mappings in complete metric spaces. Starting from the Banach contraction principle, and extend the theorems to random contractive principle. Moreover, as applications, the existence of the extremal solutions of some nonlinear functional random integral e-quations is obtained under certain conditions.