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Ball intersection model for Fejér zones of convex closed sets

Dieter Schott (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.

Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets

Nuttawut Bunlue, Suthep Suantai (2018)

Archivum Mathematicum

In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in...

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