An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces

作者：Kazmi K R^*; Bhat M I; Ahmad Naeem

来源：Journal of Computational and Applied Mathematics, 2009, 233(2): 361-371.

DOI：10.1016/j.cam.2009.07.028

• System of generalized implicit variational inclusions
• M-proximal mapping
• System of implicit Wiener-Hopf equations
• Iterative algorithm
• Convergence and stability

In this paper, we give the notion of M-proximal mapping, an extension of P-proximal mapping given in [X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369-383], for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a system of generalized implicit variational inclusions in Banach spaces and show its equivalence with a system of implicit Wiener-Hopf equations using the concept of M-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational inclusions and discuss the convergence and stability analysis of the iterative algorithm.

• 出版日期2009-11-15