Abstract
In this paper, we define some new notions of gap functions for set-valued mixed quasi-variational inequalities under suitable conditions. Further, we obtain local/global bounds for the solution of set-valued mixed quasi-variational inequality problems in terms of the residual gap function, the regularized gap function, and the D-gap function. The results obtained in this paper are generalization and refinement of previously known results for some class of variational inequality problems.
Highlights
The set-valued quasi-variational inequality problems containing the nonlinear term are definitely most notable one among the several variants of variational inequality problems
Which was studied by Gupta and Mehra [ ] and Noor [ ]. They derived local and global error bounds for the above quasi-variational inequality problems in terms of the regularized gap function and the D-gap function
In Section, we introduce a regularized gap function for SVMQVIP ( . ) and derive the error bounds with and without using the Lipschitz continuity assumption
Summary
The set-valued quasi-variational inequality problems containing the nonlinear term are definitely most notable one among the several variants of variational inequality problems. T(x), y – x ≥ , ∀y ∈ K(x), which was studied by Gupta and Mehra [ ] and Noor [ ] They derived local and global error bounds for the above quasi-variational inequality problems in terms of the regularized gap function and the D-gap function. Inspired and motivated by the recent research work above, we define some new notions of gap functions for set-valued mixed quasi-variational inequalities and obtain local/global bounds in terms of the residual, the regularized, and the D-gap function. Since this class is the most general and includes some previously studied classes of variational inequalities as special cases, our results cover and extend the previously known results. Assume that f is skew-symmetric and T is M-Lipschitz continuous with constant μ >
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 call
