Maximal Duality Mappings On Banach Spaces

Abstract

The analytical features of a Banach space K are characterized by the duality mappings on a Banach space K. One example of a monotone duality mapping on K is the subdifferential of proper convex functions on K. In this case, we look at various instances of normalized duality mappings as well as the idea of monotone operators on K. The surjectivity of the duality mappings and the notions of hemicontinuity and demicontinuity are crucial. If A and B are two monotone mappings then their sum is always monotone mapping but the sum of maximal monotone mapping may not be maximal in general. Ultimately, the circumstance that results in the sum of two maximal monotone sets becoming a maximal monotone is revealed.