A New System of Nonlinear Fuzzy Variational Inclusions Involving -Accretive Mappings in Uniformly Smooth Banach Spaces
- PDF / 596,535 Bytes
- 34 Pages / 600.05 x 792 pts Page_size
- 18 Downloads / 168 Views
Research Article A New System of Nonlinear Fuzzy Variational Inclusions Involving A, η-Accretive Mappings in Uniformly Smooth Banach Spaces M. Alimohammady,1, 2 J. Balooee,1 Y. J. Cho,3 and M. Roohi1 1
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran 2 Department of Mathematics, King’s College London Strand, London WC2R 2LS, UK 3 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea Correspondence should be addressed to Y. J. Cho, [email protected] Received 4 October 2009; Accepted 4 November 2009 Recommended by Charles E. Chidume A new system of nonlinear fuzzy variational inclusions involving A, η-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η-accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures. Copyright q 2009 M. Alimohammady 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.
1. Introduction Variational inequality was initially studied by Stampacchia 1 in 1964. In order to study many kinds of problems arising in industrial, physical, regional, economical, social, pure, and applied sciences, the classical variational inequality problems have been extended and generalized in many directions. Among these generalizations, variational inclusion introduced and studied by Hassouni and Moudafi 2 is of interest and importance. It provides us with a unified, natural, novel innovative, and general technique to study a wide class of the problems arising in different branches of mathematical and engineering sciences see, e.g., 3–7.
2
Journal of Inequalities and Applications
Next, the development of variational inequality is to design efficient iterative algorithms to compute approximate solutions for variational inequalities and their generalizations. Up to now, many authors have presented implementable and significant numerical methods such as projection method, and its variant forms, linear approximation, descent method, Newton’s method and the method based on the auxiliary principle technique. In particular, the method based on the resolvent operator technique is a generalization of the projection method and has been widely used to solve variational inclus
Data Loading...
