A pointwise contraction criteria for the existence of fixed points
Let S be a subset of a metric space (X,d) and T:S→X be a mapping. In this paper, we define the notion of lower directional increment QT(x,y] of T at x∈S in the direction of y∈X and give sufficient conditions for T to have a fixed point when QT(x,Tx]<1 for each x∈S. The results herein generalize t...
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000363 |
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| _version_ | 1850166740556709888 |
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| author | V. M. Sehgal |
| author_facet | V. M. Sehgal |
| author_sort | V. M. Sehgal |
| collection | DOAJ |
| description | Let S be a subset of a metric space (X,d) and T:S→X be a mapping. In this paper, we define the notion of lower directional increment QT(x,y] of T at x∈S in the direction of y∈X and give sufficient conditions for T to have a fixed point when QT(x,Tx]<1 for each x∈S. The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7-11) and also improve considerably some earlier results. |
| format | Article |
| id | doaj-art-de9f2f1daa7a48b78225f4d59f8780b2 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-de9f2f1daa7a48b78225f4d59f8780b22025-08-20T02:21:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012347348010.1155/S0161171279000363A pointwise contraction criteria for the existence of fixed pointsV. M. Sehgal0Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USALet S be a subset of a metric space (X,d) and T:S→X be a mapping. In this paper, we define the notion of lower directional increment QT(x,y] of T at x∈S in the direction of y∈X and give sufficient conditions for T to have a fixed point when QT(x,Tx]<1 for each x∈S. The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7-11) and also improve considerably some earlier results.http://dx.doi.org/10.1155/S0161171279000363 |
| spellingShingle | V. M. Sehgal A pointwise contraction criteria for the existence of fixed points International Journal of Mathematics and Mathematical Sciences |
| title | A pointwise contraction criteria for the existence of fixed points |
| title_full | A pointwise contraction criteria for the existence of fixed points |
| title_fullStr | A pointwise contraction criteria for the existence of fixed points |
| title_full_unstemmed | A pointwise contraction criteria for the existence of fixed points |
| title_short | A pointwise contraction criteria for the existence of fixed points |
| title_sort | pointwise contraction criteria for the existence of fixed points |
| url | http://dx.doi.org/10.1155/S0161171279000363 |
| work_keys_str_mv | AT vmsehgal apointwisecontractioncriteriafortheexistenceoffixedpoints AT vmsehgal pointwisecontractioncriteriafortheexistenceoffixedpoints |