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 ...

The main goal of this paper is to show that the problem of finding approximately a zero of a polynomial system of equations can be solved in polynomial time, on the average. The number of arithmetic operations is bounded by cN4, where N is the number of input variables and c is a universal constant. Let us be more precise. For d = (d 1, . . . , d,) each di a positive integer, let ZCd, be the li...