**MSC:**- 65J05 General theory
- 47H04 Set-valued operators, See also {28B20, 54C60, 58C06}

monotone mappings and some of their basic properties.

These properties are useful for a convergence theory of

corresponding iterative methods which are widely used to

solve convex problems. In part II the geometrical

properties of these mappings are studied. In particular the

maximal of such mappings with respect to set inclusion

of the images are investigated. The basic tool is the

representation of the images by intersection of certain

balls.