Macbeath gave a formula for the number of xed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the xed-point set of each non-identity element of a cyclic group of automorphisms acting on a closed non-orientable sur...

In this paper we formulate and prove some xed and common xed pointTheorems for self-mappings dened on complete lower Transversal functionalprobabilistic spaces.

In this paper a hybrid type theory HTT is deened which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be members of A. A xed point typing rule is given to allow for typing of xed points. The underlying theor...

The basics of a block oriented fractal image coder, are described. The output of the coder is an IFS (Iterated Function System) code, which describes the image as a xed-point of a contractive transformation. A new hierarchical interpretation of the IFS code, which relates diierent scales of the xed-point to the code, is presented and proved. The proof is based on nding a function of a continuou...

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chieey using Ky Fan's xed point principle. The main result of the paper improves Theorem 1 in 16] as well as Theorem 2.2 of 3]. Some meaningful concrete cases are also presented and discussed. KEY WORDS: operator inclusions in Banach spaces, Ky Fan's xed poi...