An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces
The notion of M-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on a Banach space is introduced. It is an extension of the P-proximal mappings given by \textit{X.\,P.\thinspace Ding} and \textit{F.\,Q.\thinspace Xia} [J.~Comput.\ Appl.\ Math.\ 147, No.\,2, 369--383 (2002; Zbl 1009.49011)]. Using the concept of M-proximal mapping, an equivalence is established between a system of generalized implicit variational inclusions and a new system of implicit Wiener-Hopf equations. A new iterative algorithm is proposed for a system of generalized implicit variational inclusions. The stability and the convergence of the iterative algorithm are established.
generalized implicit variational inclusions
scientific article; zbMATH DE number 5612607
scientific article