Viscosity Coderivatives and Their Limiting Behavior in Smooth Banach Spaces

This paper concerns with generalized differentiation of set-valued and nonsmooth mappings between Banach spaces. We study the so-called viscosity coderivatives of multifunctions and their limiting behavior under certain geometric assumptions on spaces in question related to the existence of smooth bump functions of any kind. The main results include various calculus rules for viscosity coderivatives and their topological limits. They are important in applications to variational analysis and optimization.     

A selection theorem for a new class of set-valued maps

A new class of set-valued maps that includes all upper and lower semicontinuous set-valued maps is introduced. For this class, a selection theorem having applications in the theory of differential inclusions is presented. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 503–507, October, 1999.     

完备凸度量空间中(次)相容和集值广义非扩张映象的公共不动点定理

本文在完备凸度量空间中,利用集值和单值映象(次)相容的一些条件,建立了数值广义非扩张映象存在公共不动点的一个充要条件和一个充分条件.我们的结果改进、扩充和发展了文[2～7]中的主要结果.