Main Article Content
Abstract
In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spaces. We get a C*-algebra valued metric space which get values in noncomutative operators. We demonstrate existance and uniqeness of coupled fixed point in a such space. Besides, we support our results by giving numerical examples.
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Article Details
References
- B. Blackadar. K-theory for operator Algebras MSRI Publ. 5, Cambridge University Press,13 1998
- K. R. Davidson. C-algebras by Example, Fields Institute monographs, Amer.Math. Soc.,15 Providence, 1996.
- I. Gelfand and M. Naimark, On the embedding of normed rings into the ring of operators in Hilbert space, Math. Sb. 12, 197-213, 1943.
- L.G. Huang and X. Zhang. Cone metric spaces and xed point theorems of contractive 19 mappings, J. Math. Anal. Appl.,332,1468-1476, 2007.
- Zhenhua Ma, Lining Jiang and Hongkai Sun. C- algebra valued metric spaces and realated fixed point theorems, Fixed point theory and thier applications, 206 , 1-11, 2014.
- Zhenhua Ma, Lining Jiang. C- algebra valued b-metric spaces and realated xed point 23 theorems, Fixed point theory and thier applications, 2015,222 , DOI10.1186/s13663-015- 24 0471-6.
- G. J. Murphy. C-algebras and Operator Theory, Academic Press, 1990.
- O . O zer, S. Omran. Common xed point in C -algebra b- valued metric space, In the Ap27
- plication of mathematics n technical and natural scences: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16),
- (1). 050005. AIP Publishing,2016, https:/doi.org/10.1063/1.4964975.
- O . O zer, S. Omran, On the generalized C - valued metric spaces related with Banach fixed point theory, International Journal of Advanced and Applied Sciences, Vol.4(2), 35-37, 2017,
- https://doi.org/10.21833/ijaas.2017.02.006.
- G. K. Pedersen. C-algebras and their automorphism groups, Academic Press,London, 1979.
- X. Qiaoling, J.Lining, M. Zhenhua.Common xed point theorems in C algebra valued metricspaces, ,arXiv : 1560.05545v2 [math.FA] 30 Jun 2015.
- Sh. Rezapour and R.Hamlbarani. Some notes on the paper "cone metric spaces and xedpoint theorems of contractive mappings, J. Math. Anal. Appl., 345:719 -724, 2008.
- Ahmed El-1 Sayed , Saleh Omran and Abdalla Asad, Fixed point Theorems in Quaternion -Valued metric spaces,Abstract and applied analysis, 2014.
- C. Tianqing. Some coupled xed point theorems in C-algebra valued metric spaces,arXiv :1601.07168v1 [math.OA] 26 Jan 2016.
References
B. Blackadar. K-theory for operator Algebras MSRI Publ. 5, Cambridge University Press,13 1998
K. R. Davidson. C-algebras by Example, Fields Institute monographs, Amer.Math. Soc.,15 Providence, 1996.
I. Gelfand and M. Naimark, On the embedding of normed rings into the ring of operators in Hilbert space, Math. Sb. 12, 197-213, 1943.
L.G. Huang and X. Zhang. Cone metric spaces and xed point theorems of contractive 19 mappings, J. Math. Anal. Appl.,332,1468-1476, 2007.
Zhenhua Ma, Lining Jiang and Hongkai Sun. C- algebra valued metric spaces and realated fixed point theorems, Fixed point theory and thier applications, 206 , 1-11, 2014.
Zhenhua Ma, Lining Jiang. C- algebra valued b-metric spaces and realated xed point 23 theorems, Fixed point theory and thier applications, 2015,222 , DOI10.1186/s13663-015- 24 0471-6.
G. J. Murphy. C-algebras and Operator Theory, Academic Press, 1990.
O . O zer, S. Omran. Common xed point in C -algebra b- valued metric space, In the Ap27
plication of mathematics n technical and natural scences: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16),
(1). 050005. AIP Publishing,2016, https:/doi.org/10.1063/1.4964975.
O . O zer, S. Omran, On the generalized C - valued metric spaces related with Banach fixed point theory, International Journal of Advanced and Applied Sciences, Vol.4(2), 35-37, 2017,
https://doi.org/10.21833/ijaas.2017.02.006.
G. K. Pedersen. C-algebras and their automorphism groups, Academic Press,London, 1979.
X. Qiaoling, J.Lining, M. Zhenhua.Common xed point theorems in C algebra valued metricspaces, ,arXiv : 1560.05545v2 [math.FA] 30 Jun 2015.
Sh. Rezapour and R.Hamlbarani. Some notes on the paper "cone metric spaces and xedpoint theorems of contractive mappings, J. Math. Anal. Appl., 345:719 -724, 2008.
Ahmed El-1 Sayed , Saleh Omran and Abdalla Asad, Fixed point Theorems in Quaternion -Valued metric spaces,Abstract and applied analysis, 2014.
C. Tianqing. Some coupled xed point theorems in C-algebra valued metric spaces,arXiv :1601.07168v1 [math.OA] 26 Jan 2016.