Nj. Huang, A new class of generalized set-valued implicit variational inclusions in Banach spaces with an application, COMPUT MATH, 41(7-8), 2001, pp. 937-943
In this paper, we introduce and study a new class of generalized set-valued
implicit variational inclusions in real Banach spaces. By using Nadler's T
heorem and the resolvent operator technique for m-accretive mapping in real
Banach spaces, we construct some new iterative algorithms for solving this
class of generalized set-valued implicit variational inclusions. We prove
the existence of solution for this kind of generalized set-valued implicit
variational inclusions without compactness and the convergence of iterative
sequences generated by the algorithms in Banach spaces. We also give an ap
plication to generalized set-valued implicit variational inequalities in re
al Hilbert spaces. (C) 2001 Elsevier Science Ltd. All rights reserved.