Fixed points of a certain class of mappings in spaces with uniformly normal structure
A fixed point theorem is proved in a Banach space E which has uniformly normal structure for asymptotically regular mapping T satisfying: for each x,y in the domain and for n=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖), where an,bn,cn are nonnegative constants satisfying certain...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000933 |
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| _version_ | 1832552261324111872 |
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| author | Jong Soo Jung Balwant Singh Thakur Daya Ram Sahu |
| author_facet | Jong Soo Jung Balwant Singh Thakur Daya Ram Sahu |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | A fixed point theorem is proved in a Banach space E which has uniformly normal
structure for asymptotically regular mapping T satisfying:
for each x,y in the domain and for
n=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖),
where an,bn,cn are nonnegative constants satisfying certain conditions. This result generalizes a fixed
point theorem of Górnicki [1]. |
| format | Article |
| id | doaj-art-d3b98e4a8c604e4e9ce4f88f3f6ab526 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d3b98e4a8c604e4e9ce4f88f3f6ab5262025-02-03T05:59:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121467768010.1155/S0161171298000933Fixed points of a certain class of mappings in spaces with uniformly normal structureJong Soo Jung0Balwant Singh Thakur1Daya Ram Sahu2Department of Mathematics, Dong-A University, Pusan 607-714, KoreaGovt. B. H. S. S. Gariaband, Dist. Raipur, 493889, M. P., IndiaGovt. H. S. S. Kumhari, Dist. Durg, 490042, M. P., IndiaA fixed point theorem is proved in a Banach space E which has uniformly normal structure for asymptotically regular mapping T satisfying: for each x,y in the domain and for n=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖), where an,bn,cn are nonnegative constants satisfying certain conditions. This result generalizes a fixed point theorem of Górnicki [1].http://dx.doi.org/10.1155/S0161171298000933Uniformly normal structureasymptotic regularityfixed point. |
| spellingShingle | Jong Soo Jung Balwant Singh Thakur Daya Ram Sahu Fixed points of a certain class of mappings in spaces with uniformly normal structure International Journal of Mathematics and Mathematical Sciences Uniformly normal structure asymptotic regularity fixed point. |
| title | Fixed points of a certain class of mappings in spaces with uniformly normal structure |
| title_full | Fixed points of a certain class of mappings in spaces with uniformly normal structure |
| title_fullStr | Fixed points of a certain class of mappings in spaces with uniformly normal structure |
| title_full_unstemmed | Fixed points of a certain class of mappings in spaces with uniformly normal structure |
| title_short | Fixed points of a certain class of mappings in spaces with uniformly normal structure |
| title_sort | fixed points of a certain class of mappings in spaces with uniformly normal structure |
| topic | Uniformly normal structure asymptotic regularity fixed point. |
| url | http://dx.doi.org/10.1155/S0161171298000933 |
| work_keys_str_mv | AT jongsoojung fixedpointsofacertainclassofmappingsinspaceswithuniformlynormalstructure AT balwantsinghthakur fixedpointsofacertainclassofmappingsinspaceswithuniformlynormalstructure AT dayaramsahu fixedpointsofacertainclassofmappingsinspaceswithuniformlynormalstructure |