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Brouwer Fixed Point Theorem for Simplexes

Karol Pąk (2011)

Formalized Mathematics

In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the notion of a bounded simplicial complex and the diameter of a bounded simplicial complex. We also prove...

Brouwer Fixed Point Theorem in the General Case

Karol Pąk (2011)

Formalized Mathematics

In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εn with a non empty interior. This article is based on [15].

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. Pathak, Shin Min Kang, Yeol Je Cho (1998)

Czechoslovak Mathematical Journal

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.

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