Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings
The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstra...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/786814 |
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| author | R. K. Bisht |
| author_facet | R. K. Bisht |
| author_sort | R. K. Bisht |
| collection | DOAJ |
| description | The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem. |
| format | Article |
| id | doaj-art-e14c45adf21348bf935965c229558370 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e14c45adf21348bf935965c2295583702025-02-03T01:27:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/786814786814Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive MappingsR. K. Bisht0Department of Mathematics, Kumaun University, D. S. B. Campus, Nainital 263002, IndiaThe aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.http://dx.doi.org/10.1155/2012/786814 |
| spellingShingle | R. K. Bisht Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings International Journal of Mathematics and Mathematical Sciences |
| title | Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings |
| title_full | Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings |
| title_fullStr | Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings |
| title_full_unstemmed | Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings |
| title_short | Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings |
| title_sort | common fixed points of generalized meir keeler type condition and nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2012/786814 |
| work_keys_str_mv | AT rkbisht commonfixedpointsofgeneralizedmeirkeelertypeconditionandnonexpansivemappings |