涉及拟反向强单调算子零点的一个弱收敛结果及其应用

A weak convergence theorem involving the zero point of quasi-inverse strongly monotone operators with application

采用经典的最速下降法构造一类Lipschitz连续的拟反向强单调算子的零点,在相当宽松柔和的条件下,建立了一个弱收敛结果。将弱收敛定理应用于分裂公共不动点问题,所得结果改进了近期文献的相应结果。

In this paper,the classical steepest descent method has been used to construct the zeros of a class of Lipschitz continuous and quasi-inverse strongly monotone operators.Under very mild conditions,a weak convergence theorem is established.Applying our weak convergence theorem to the split common fixed point problem,some new results are deduced which improve the recent known results in literature.