Dieter Schott
Strongly Fej\'{e}er monotone mappings
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

65J05 General theory

47H04 Set-valued operators, See also {28B20, 54C60, 58C06}

Abstract: We consider the general class of strongly Fej\'{e}r
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.
Keywords: Set-valued mappings, Fej\'{e}r monotone mappings, relaxations, central stretching, convex sets, ball intersections