A Kakutani type coincidence theorem

A Lefschetz-type Coincidence Theorem

A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg, that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y ...

Markov-Kakutani Theorem and Haar Measure

The Interprocedural Coincidence Theorem

We present an interprocedural generalization of the well-known (intraprocedural) Coincidence Theorem of Kam and Ullman, which provides a suucient condition for the equivalence of the meet over all paths (MOP) solution and the maximal xed point (MFP) solution to a data ow analysis problem. This generalization covers arbitrary imperative programs with recursive procedures, global and local variab...

Caristi Type Coincidence Point Theorem in Topological Spaces

The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...

A Note on Kakutani Type Fixed Point Theorems

We present Kakutani type fixed point theorems for certain semigroups of self maps by relaxing conditions on the underlying set, family of self maps, and the mappings themselves in a locally convex space setting.