GNM ordered variational inequality system with ordered Lipschitz continuous mappings in an ordered Banach space
Honggang Li, Dong Qiu, Mao-Ming Jin · Journal of Inequalities and Applications · 2013
The main purpose of this paper is to introduce and study a new class of generalized nonlinear mixed ordered variational inequalities systems with ordered Lipschitz continuous mappings in ordered Banach spaces. Then, applying the matrix analysis and the vector-valued mapping fixed point analysis method, an existence theorem of solutions for this kind of the system is established. Furthermore, based on the existence theorem and the new ordered B -restricted-accretive mappings, a general algorithm for solving the systems is introduced and applied to the approximation solvability of the systems on hand. The obtained results seem to be general in nature. MSC: 49J40, 47H06.