Characterizations of weak-ANODD set-valued mappings with applications to an approximate solution of GNMOQV inclusions involving ⊕ operator in ordered Banach spaces
Hong Gang Li, Dong Qiu, Yang Zou · Fixed Point Theory and Applications · 2013
In ordered Banach spaces, characterizations of ordered -weak-ANODD set-valued mappings are introduced and studied, which is applied to giving an approximate solution for a new class of general nonlinear mixed-order quasi-variational inclusions involving ⊕ operator. By using the resolvent operator associated with an -weak-ANODD set-valued mapping and fixed point theory, an existence theorem of solutions and an approximation algorithm for this kind of inclusions are established and discussed in ordered Banach spaces, and the relation between the first-valued point and the solution of the problems is shown. The results obtained seem to be general in nature. MSC:49J40, 47H06.