Generalized set-valued nonlinear variational-like inequalities
Balwant Singh Thakur, Suja Varghese · 2013
In this paper, we study a new class of generalized set-valued nonlinear variational-like inequalities (GSNVLI) in Hilbert spaces. By ap- plying the auxiliary principle technique, we establish existence and unique- ness theorem for a solution of (GSNVLI) problem. We further suggest an algorithm to obtain a solution of (GSNVLI) problem and establish a convergence result in which sequence generated by the proposed algorithm converges to a solution of the (GSNVLI) problem. Our results represent renement and improvement of the previously known results in variational inequalities.