Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications
The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M.,Öz...
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| Language: | English |
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De Gruyter
2017-11-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0028/dema-2017-0028.xml?format=INT |
| _version_ | 1828787670341386240 |
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| author | Tomar Anita Beloul Said Sharma Ritu Upadhyay Shivangi |
| author_facet | Tomar Anita Beloul Said Sharma Ritu Upadhyay Shivangi |
| author_sort | Tomar Anita |
| collection | DOAJ |
| description | The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M.,Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput.Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for twoweakly compatible pairs of self mappings. In the sequelwe also answer affirmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 2011, 25(2), 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates. |
| first_indexed | 2024-12-12T00:36:43Z |
| format | Article |
| id | doaj.art-b30b7c83228f4893a769a46f8ce81f8d |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-12T00:36:43Z |
| publishDate | 2017-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-b30b7c83228f4893a769a46f8ce81f8d2022-12-22T00:44:21ZengDe GruyterDemonstratio Mathematica2391-46612017-11-0150127829810.1515/dema-2017-0028dema-2017-0028Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applicationsTomar Anita0Beloul Said1Sharma Ritu2Upadhyay Shivangi3Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar(Uttarakhand), IndiaDepartment of Mathematics, University of El-Oued, P. O. Box 789, El-Oued 39000, AlgeriaDepartment of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), IndiaDepartment of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), IndiaThe aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M.,Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput.Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for twoweakly compatible pairs of self mappings. In the sequelwe also answer affirmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 2011, 25(2), 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates.http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0028/dema-2017-0028.xml?format=INTCommon fixed pointweakly compatiblegeneralized condition (B)partial-metric spacequasipartial metric space47H1054H25 |
| spellingShingle | Tomar Anita Beloul Said Sharma Ritu Upadhyay Shivangi Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications Demonstratio Mathematica Common fixed point weakly compatible generalized condition (B) partial-metric space quasipartial metric space 47H10 54H25 |
| title | Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications |
| title_full | Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications |
| title_fullStr | Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications |
| title_full_unstemmed | Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications |
| title_short | Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications |
| title_sort | common fixed point theorems via generalized condition b in quasi partial metric space and applications |
| topic | Common fixed point weakly compatible generalized condition (B) partial-metric space quasipartial metric space 47H10 54H25 |
| url | http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0028/dema-2017-0028.xml?format=INT |
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