Banach空间中一类集值变分包含解的存在与逼近问题

Existence and Approximation Problems of Solutions to A Class of Set-valued Variational Inclusions in Banach Spaces

本文介绍和研究了Banach空间中的一类带有Φ -强增生条件的集值变分包含解的存在性与逼近问题 .通过推广参考文献 [6 ]中的 η -次微分的概念 ,利用Michael的连续选择定理以及单值情形的相应结果 ,建立了集值变分包解的存在性定理 ,以及参考文献 [7]中的带有混合误差的Ishikawa迭代序列强收敛到集值变分包含解的一个充要条件 .所得结果推广和改进了参考文献 [1],[3],[5 ],[9],[10

In this paper,we introduce and study the existence and approximation problems of solutions to a class set-valued variational inclusions with Φ-strongly accretive mappings in Banach spaces.By generalizing the conception of η-subdifferential in and using Michael's continuous selection theorem and the corresponding results of single-value variational inclusions,we establish the existence theorem of solutions,and obtain a necessary and sufficient condition on which the Ishikawa iterative sequence with mixed errors converges strongly to the solutions of variational inclusions.These results generalize and improve corresponding results in ,,,,.