Year-end Sale % OFF 
Abstract
In this paper, the approximate solvability for a system of generalized relaxed cocoercive nonlinear variational inequalities in Hilbert spaces is studied, based on the convergence of the projection methods. The results presented in this paper extend and improve the main results of Refs. (Verma in Comput. Math. Appl. 41:1025-1031, 2001; Verma in Int. J. Differ. Equ. Appl. 6:359-367, 2002; Verma in J. Optim. Theory Appl. 121(1):203-210, 2004; Verma in Appl. Math. Lett. 18(11):1286-1292, 2005; Chang, Lee and Chan in Appl. Math. Lett. 20:329-334, 2007).MSC:90C33, 65K15, 58E36.
Highlights
1 Introduction Variational inequalities are one of the most interesting and intensively studied classes of mathematical problems and there exists a considerable amount of literature [ – ] on the approximate solvability of nonlinear variational inequalities
The results presented in this paper extend and improve the main results in [ – ]
Throughout this paper, we assume that H is a real Hilbert space with the inner product ·, · and the induced norm ·
Summary
Variational inequalities are one of the most interesting and intensively studied classes of mathematical problems and there exists a considerable amount of literature [ – ] on the approximate solvability of nonlinear variational inequalities. We consider a system of generalized nonlinear variational inequality (SGNVI) problem as follows: find an element (x∗, y∗) ∈ C × C such that λT (y∗, x∗) + g (x∗) – f (y∗), x – g (x∗) ≥ , ∀x ∈ C and λ > , μT (x∗, y∗) + g (y∗) – f (x∗), x – g (y∗) ≥ , ∀x ∈ C and μ > .
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
