A generalization of some fixed point theorems of K. M. Ghosh
This note establishes the following result. Let T be a selfmap of a normed linear space E. For 0<λ≤1, define Tλx=λx+(1−λ)Tx for each x in E. If, in addition, S=TTλ satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TTλu=TλTu, then u is...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000192 |
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| _version_ | 1832545327854387200 |
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| author | B. E. Rhoades |
| author_facet | B. E. Rhoades |
| author_sort | B. E. Rhoades |
| collection | DOAJ |
| description | This note establishes the following result. Let T be a selfmap of a normed linear space E. For 0<λ≤1, define Tλx=λx+(1−λ)Tx for each x in E. If, in addition, S=TTλ satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TTλu=TλTu, then u is the unique fixed point for T. |
| format | Article |
| id | doaj-art-b500c00651b44533946743f05361e591 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b500c00651b44533946743f05361e5912025-02-03T07:26:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015120320310.1155/S0161171282000192A generalization of some fixed point theorems of K. M. GhoshB. E. Rhoades0Mathematics Department, Indiana University, Bloomington 47405, Indiana, USAThis note establishes the following result. Let T be a selfmap of a normed linear space E. For 0<λ≤1, define Tλx=λx+(1−λ)Tx for each x in E. If, in addition, S=TTλ satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TTλu=TλTu, then u is the unique fixed point for T.http://dx.doi.org/10.1155/S0161171282000192fixed pointmean value iteration. |
| spellingShingle | B. E. Rhoades A generalization of some fixed point theorems of K. M. Ghosh International Journal of Mathematics and Mathematical Sciences fixed point mean value iteration. |
| title | A generalization of some fixed point theorems of K. M. Ghosh |
| title_full | A generalization of some fixed point theorems of K. M. Ghosh |
| title_fullStr | A generalization of some fixed point theorems of K. M. Ghosh |
| title_full_unstemmed | A generalization of some fixed point theorems of K. M. Ghosh |
| title_short | A generalization of some fixed point theorems of K. M. Ghosh |
| title_sort | generalization of some fixed point theorems of k m ghosh |
| topic | fixed point mean value iteration. |
| url | http://dx.doi.org/10.1155/S0161171282000192 |
| work_keys_str_mv | AT berhoades ageneralizationofsomefixedpointtheoremsofkmghosh AT berhoades generalizationofsomefixedpointtheoremsofkmghosh |