International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3645-3659
doi:10.1155/IJMMS.2005.3645

Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces

Yali Zhao,1,2 Zunquan Xia,1 and Zeqing Liu3

1Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China
2Department of Mathematics and Computer Science, Chaoyang Teachers College, Chaoyang, Liaoning 122000, China
3Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, China

Received 23 March 2005; Revised 16 September 2005

Copyright © 2005 Yali Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the generalized set-valued variational-like inclusions in reflexive Banach spaces. The results presented in this paper are new and are an extension of the corresponding results in this direction.