It follows from Browder (Summa Bras Math 4:183–191, 1960) that for every continuous function $$F : (X \times Y) \rightarrow Y$$ , where X is the unit interval and Y a nonempty, convex, compact subset of locally convex linear vector space, set fixed points F, defined by $$C_F := \{ (x,y) \in :F(x,y)=y\}$$ has connected component whose projection to first coordinate X. We extend Browder’s result ...

Let X be a non-locally convex F-space (complete metric linear space) whose dual X' separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space XIN does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

We present locally-linear learning machines (L3M) for multi-class classification. We formulate a global convex risk function to jointly learn linear feature space partitions and region-specific linear classifiers. L3M’s features such as: (1) discriminative power similar to Kernel SVMs and Adaboost; (2) tight control on generalization error; (3) low training time cost due to on-line training; (4...

In the previous paper ([5]), we studied the ordinary multiobjective convex program on a locally convex linear topological space in the case that the objective functions and the constraint functions were continuous and convex, but not always Gateaux differ entiable. In the case, we showed that the generalized Kuhn-Tucker conditions given by a subdifferential formula were necessary and sufficient...

This paper introduces a new technique for proving the local optimality of packing configurations of Euclidean space. Applying this technique to a general convex polygon, we prove that under mild assumptions satisfied generically, the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also locally optimal in the full space of packings.

In this paper the following phenomena of geodesics in an innnite-dimensional Teichm uller space are founded: a geodesic (locally shortest arc) need not be a straight line (an isometric embedding of a segment of R into the Teichm uller space), no sphere is convex with respect to straight lines, and some geodesics can intersect themselves.

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories — in particular, the standard cosimplicial topological space can be produced.

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...