McMullen’s proof of the Hard Lefschetz Theorem for simple polytopes is studied, and a new proof of this theorem that uses conewise polynomial functions on a simplicial fan is provided.

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which composed nonlinear equation with Atangana-Baleanu derivative and time-dependent inequality. We explore an existence uniqueness theorem for the under consideration. Our proof based on F-KKM theorem, Banach fixed point principle, theory monotone operators.

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solutio...

From results of Ishihara it is known that the weak (that is, binary) form of König’s lemma (WKL) implies Brouwer’s fan theorem (Fan). Moreover, Berger and Ishihara [MLQ 2005] have shown that a weakened form WKL! of WKL, where as an additional hypothesis it is required that in an effective sense infinite paths are unique, is equivalent to Fan. The proof that WKL! implies Fan is done explicitely....

Karasek's job strain model postulates that workers chronically exposed to adverse psychosocial work environment (high strain job)--high psychological job demands and low job control, including poor social support, increased physical demand and hazardous work condition--will eventually develop both physical illnesses such as cardiovascular diseases and psychological disorders such as depression....

In this paper, we present some fixed point theorems for generalized condensing multimaps on KKM uniform spaces. We also obtain some new fixed point results for generalized condensing multimaps in KC class (or KKM class) in the setting of abstract convex uniform spaces. Mathematics Subject Classification: 47H10, 47H04, 46A16, 52A07, 54C60, 54H25, 55M20

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which suffices...

Code equivalence is a basic concept in coding theory. The well-known theorem by MacWilliams gives a sufficient condition for code equivalence. Recently the MacWilliams theorem has been generalized, by Fan, Liu and Puig, making use of the generalized Hamming weights (GHWs). In this paper, we will present a further generalization of the MacWilliams theorem. Our result extends both the MacWilliams...