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}...

Correspondence: [email protected] Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, P. R China Abstract In this article, we prove the existence of solutions for the general variational inequality j(x, y) ≥ f(x) f(y) and Minty type theorem by using the generalized KKM theorem in topological spaces without linear structure. Some properties of solutions set for t...

In this paper, we study the existence of solutions for vector saddle points problems in a general setting. Our approach, first, is based on the KKM lemma and a relaxation of the C− lower semicontinuity notion introduced by T.Tanaka by means of an extension to the vector setting of a Bŕezis-NirenbergStampacchia condition, and arguments from generalized convexity. This leads us to generalize and ...

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalizedmixed equilibriumproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed ...

In this paper, we studied a new kind of vector equilibrium problem, we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and KKM theorem these two tools,then we generalized this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds is a open problem proposed by Isac, Sehgal and Singh in 1999....

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η − α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the so...

* Correspondence: [email protected]. th Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Abstract In this article, we consider the solutions of the system of generalized variational inequality problems in Banach spaces. By employing the generalized projection operator, the well-known Fan’s KKM theorem and Kakutani-Fan-Glicksberg fixed point theorem, we...