Journal of Optimization Theory and Applications

, Volume 158, Issue 2, pp 615–625 | Cite as

Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces



In this work, we consider two classes of non-self-mappings, which are called proximal weakly contractive and proximal nonexpansive mappings, and study the existence of solutions of a minimization problem. Existence results of best proximity points for these two classes of non-self-mappings in metric and Banach spaces are also obtained.


Proximal weakly contractive Proximal nonexpansive Best proximity point P-property 



The author thanks anonymous referees and the handling editor, professor Franco Giannessi, for their helpful remarks and suggestions that allowed him to improve the original presentation.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsAyatollah Boroujerdi UniversityBoroujerdIran

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