Some fixed point theorems for set valued directional contraction mappings
Let S be a subset of a metric space X and let B(X) be the class of all nonempty bounded subsets of X with the Hausdorff pseudometric H. A mapping F:S→B(X) is a directional contraction iff there exists a real α∈[0,1) such that for each x∈S and y∈F(x), H(F(x),F(z))≤αd(x,z) for each z∈[x,y]∩S, where [x...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000336 |
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| _version_ | 1849399032120606720 |
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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 and let B(X) be the class of all nonempty bounded subsets of X with the Hausdorff pseudometric H. A mapping F:S→B(X) is a directional contraction iff there exists a real α∈[0,1) such that for each x∈S and y∈F(x), H(F(x),F(z))≤αd(x,z) for each z∈[x,y]∩S, where [x,y]={z∈X:d(x,z)+d(z,y)=d(x,y)}. In this paper, sufficient conditions are given under which such mappings have a fixed point. |
| format | Article |
| id | doaj-art-9db86889443244d7a7764c440f8b2f36 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9db86889443244d7a7764c440f8b2f362025-08-20T03:38:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013345546010.1155/S0161171280000336Some fixed point theorems for set valued directional contraction mappingsV. M. Sehgal0Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USALet S be a subset of a metric space X and let B(X) be the class of all nonempty bounded subsets of X with the Hausdorff pseudometric H. A mapping F:S→B(X) is a directional contraction iff there exists a real α∈[0,1) such that for each x∈S and y∈F(x), H(F(x),F(z))≤αd(x,z) for each z∈[x,y]∩S, where [x,y]={z∈X:d(x,z)+d(z,y)=d(x,y)}. In this paper, sufficient conditions are given under which such mappings have a fixed point.http://dx.doi.org/10.1155/S0161171280000336directional contractionHausdorff pseudometric. |
| spellingShingle | V. M. Sehgal Some fixed point theorems for set valued directional contraction mappings International Journal of Mathematics and Mathematical Sciences directional contraction Hausdorff pseudometric. |
| title | Some fixed point theorems for set valued directional contraction mappings |
| title_full | Some fixed point theorems for set valued directional contraction mappings |
| title_fullStr | Some fixed point theorems for set valued directional contraction mappings |
| title_full_unstemmed | Some fixed point theorems for set valued directional contraction mappings |
| title_short | Some fixed point theorems for set valued directional contraction mappings |
| title_sort | some fixed point theorems for set valued directional contraction mappings |
| topic | directional contraction Hausdorff pseudometric. |
| url | http://dx.doi.org/10.1155/S0161171280000336 |
| work_keys_str_mv | AT vmsehgal somefixedpointtheoremsforsetvalueddirectionalcontractionmappings |