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...

The inequality Ffx;fy(qs) Fx;y(s) (s 0), where q 2 (0; 1), is generalized for multivalued mappings in many directions. Using Hausdor distance S.B. Nadler in [7] introduced a generalization of Banach contraction principle in metric spaces. In [3] the de nition of probabilistic Nadler q-contraction is given. Using some results given in [12] a xed point theorem on spaces with a convex structure is...

For every xed-point expression e of alternation-depth r, we construct a new xed-point expression e 0 of alternation-depth 2 and size O(r jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We show that our transformation is optimal not only w.r.t. alternation-depth but also w.r.t. the increase in ...

We give a new proof for the existence of a non{Gaussian hierarchical renormalization group xed point, using what could be called a beta{function for this problem. We also discuss the asymptotic behavior of this xed point, and the connection between the hierarchical models of Dyson and Gallavotti. 1 Supported in Part by the National Science Foundation under Grant No. DMS{8802590. 2 Supported in ...

We report on our recent studies of the large N renormalization group (RG) method which clariies phase structure of random matrix models. We derive an exact RG equation which enables us to obtain the exact locations of xed points and their scaling exponents. The classiication of phases is given by this analysis. A linear approximation visualizes the RG ow of crossover phenomena including several...

Xia’s algorithm consists of a reduction algorithm and a translation procedure both originally used to tackle the xed point property for ordered sets. We present results that show that the translation procedure allows access to a much wider range of problems and results showing that the algorithm is very e cient when applied to the xed point property in ordered sets or for order=graph isomorphis...