Extending monotone mappings

Extending Mappings between Posets

A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with possibly associated initial and/or boundary value problems. 1. The General Setup Let (X,≤) and (Y,≤) be two arbitrary posets and (1.1) φ : X −→ Y any mappin...

Quasiconformal Geometry of Monotone Mappings

This paper concerns a class of monotone mappings in a Hilbert space that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling-Ahlfors extension and from Brenier’s polar factorization, and find applications in the geometry of metric spaces and ...

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Convergence Theorems for Nonexpansive Mappings and Inverse-strongly Monotone Mappings

In this paper, we introduce a general iterative scheme for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping.

Cone Monotone Mappings: Continuity and Differentiability

We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and coneto-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (...