构造非线性极大单调映象方程极小范数解的广义预解式迭代过程

Generalized Resolvent iteration Processes for Maximal Monotone Operators Equation in Banach Spaces

本文定义了求极大单调映象方程o∈Ax解的一个广义预解式迭代过程,并证明了所定义的迭代过程对该方程极小范数解的收敛性,所得结果改进并推广了R.T.Rockafcller[1],G.Kassay[8]等的基本收敛性定理。

As an extension of R.T.Rockafcllar's proximal point algorithm for maximal monotone operators equation in Hilbert space, the authors propose a generalized resolvent iteration processes for the same problem in a reflexive Banach space X. It is proved that the generalized processes can be used to construct the minimum-norm solution of nonlinear operators equation 0∈Axwith A being an arbitrary maximal monotone mapping from X to X* .The convergence results obtained here provides not only a modification on Rockefellar's and G.assay's (Cf.[l], [8]), but also a partial answer to F.E.Browder's problem on constructively solvability for monotone mappings.