The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contract...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/375604 |
| Summary: | Recently, Basha (2011) established the best proximity point theorems for
proximal contractions of the first and second kinds which are extension of Banach's contraction
principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the
notions of proximal contractions of the first and second kinds which are more general than the
notion of self-contractions, establish the existence of an optimal approximate solution theorems
for these non-self-mappings, and also give examples to validate our main results. |
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| ISSN: | 1085-3375 1687-0409 |