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

✍ Scribed by K.R. Kazmi; M.I. Bhat; Naeem Ahmad

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 751 KB
Volume: 233
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.07.028

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✦ Synopsis

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 quasivariational 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.

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