In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.
The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.
