We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases. By applying the auxiliary principle technique and KKM theory, we suggest an iterative algorithm for solving the generalized strongly nonlinear mixed variationallike inequality. The exi...

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

We introduce the notion of a matrad M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrads and its inverse, the universal enveloping functor. We define the free matrad H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...