Metric Subregularity For A Multif-unction In A Banach Space

In this paper, we mainly study the metric subregularity for a multifunction in a Banach space. Ioffe[Trans. Amer. Math. Soc.,251(1979), pp.61-69.] provid-ed a sufficient condition for the metric subregularity in terms of the subdifferential mapping in the special case of a local Lipschitz real function. Zheng and Ng[SIAM J. Optim.,20(2010), pp.2119-2136.] extended the Ioffe’s result to a general mul-tifunction. Subsequently, Zheng and He[Nonlinear Anal.,100(2014), pp.116-127.] generalized the result of Zheng and Ng again. This paper further improves Zheng and He’s result, and obtains much sharper results in the case of Asplund space and Frechet smooth Banach space.