Results on the Existence and Convergence of Best Proximity Points
<p/> <p>We first consider a cyclic <inline-formula> <graphic file="1687-1812-2010-386037-i1.gif"/></inline-formula>-contraction map on a reflexive Banach space <inline-formula> <graphic file="1687-1812-2010-386037-i2.gif"/></inline-for...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
|
| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/386037 |
| Summary: | <p/> <p>We first consider a cyclic <inline-formula> <graphic file="1687-1812-2010-386037-i1.gif"/></inline-formula>-contraction map on a reflexive Banach space <inline-formula> <graphic file="1687-1812-2010-386037-i2.gif"/></inline-formula> and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic <inline-formula> <graphic file="1687-1812-2010-386037-i3.gif"/></inline-formula>-contraction maps in reflexive Banach spaces in one of their works (2009). In the second part of the paper, we will discuss the existence of best proximity points in the framework of more general metric spaces. We obtain some new results on the existence of best proximity points in hyperconvex metric spaces as well as in ultrametric spaces.</p> |
|---|---|
| ISSN: | 1687-1820 1687-1812 |