Sets that remain maximal monotone under all monotone perturbations

Perturbations of Nonlinear Maximal Monotone Sets in Banach Space *

Records, the Maximal Layer, and Uniform Distributions in Monotone Sets

Abatract-Consider a nondecreasing nonnegative integrable function f on [0,1]. Draw an independent sample (X1,Y1) ..... (Xn,Yn) of size n from the uniform distribution under f, and let Nn be the number of records in the sample, where (Xi,Yi) is a record when, for all j # i, either Xj > Xi or l~ < Yi. We study the dependence upon f of the constant C in the asymptotic formula ENn " CV/'ff, and sho...

Extracting of All Maximal Cliques: Monotone System Approach

NP-complicated problems have been described in the graph theory. An example is the extracting of all maximal cliques from a graph. Many algorithms for solving this problem have been described. However, complexity is linear to the number of maximal cliques. This paper discusses a new approach for extracting maximal cliques, based on the monotone system theory. The complexity of the presented alg...

Positive sets and monotone sets

In this paper, we show how convex analysis can be applied to the theory of sets that are “positive” with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fi...

Solution of the Hammerstein Equations under Non–monotone Perturbations

The aim of this note is to study convergence and convergence rates of the regularized solutions for the operator equation of Hammerstein type x + F2F1(x) = f in reflexive Banach spaces under the non-monotone perturbations F h 2 and F h 1 of the operators F2 and F1, respectively.