C*-代数值度量空间中公共耦合不动点定理
Common Coupled Fixed Point Theorems in C*-Algebra-Valued Metric Spaces
DOI: 10.12677/AAM.2021.101025, PDF, 下载: 644  浏览: 773  国家自然科学基金支持
作者: 辛巧玲*：天津师范大学，数学科学学院，天津；曹天庆：天津工业大学，数学科学学院，天津
关键词: 耦合重合点； 不动点； C*-代数； 正元；Coupled Coincidence Point； Fixed Point； C*-Algebra； Positive Element
摘要: 本文给出了完备的C∗-代数值度量空间上不同压缩映射的公共耦合不动点定理。作为应用，证明了Fredholm非线性积分算子解的存在唯一性。
Abstract: In this paper, we prove some common coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete C∗-algebra-valued metric spaces. Moreover, the paper provides an application to prove the existence and uniqueness of a solution for Fredholm nonlinear integral equations.
文章引用：辛巧玲, 曹天庆. C*-代数值度量空间中公共耦合不动点定理[J]. 应用数学进展, 2021, 10(1): 218-229. https://doi.org/10.12677/AAM.2021.101025

参考文献

[1] Aydi, H., Samet, B. and Vetro, C. (2011) Coupled Fixed Point Results in Cone Metric Spaces for Compatible Mappings. Fixed Point Theory and Applications, 2011, Article No. 27.
https://doi.org/10.1186/1687-1812-2011-27
[2] Bhaskar, T.G. and Lakshmikantham, V. (2006) Fixed Point Theorems in Partially Ordered Metric Spaces and Applications. Nonlinear Analysis: Theory, Methods and Applications, 65, 1379-1393.
https://doi.org/10.1016/j.na.2005.10.017
[3] Jleli, M. and Samet, B. (2012) On Positive Solutions for a Class of Singular Nonlinear Fractional Differential Equations. Boundary Value Problems, 2012, Article No. 73.
https://doi.org/10.1186/1687-2770-2012-73
[4] Nieto, J.J. and Rodriguez-Lopez, R. (2007) Existence and Uniqueness of Fixed Point in Par- tially Ordered Sets and Applications to Ordinary Differential Equations. Acta Mathematica Sinica, English Series, 23, 2205-2212.
https://doi.org/10.1007/s10114-005-0769-0
[5] Ran, A.C.M. and Reurings, M.C.B. (2004) A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations. Proceedings of the American Mathematical Soci- ety, 132, 1435-1443.
https://doi.org/10.1090/S0002-9939-03-07220-4
[6] Guo, D. and Lakshmikantham, V. (1987) Coupled Fixed Points of Nonlinear Operators with Applications. Nonlinear Analysis: Theory, Methods and Applications, 11, 623-632.
https://doi.org/10.1016/0362-546X(87)90077-0
[7] Luong, N.V. and Thuan, N.X. (2011) Coupled Fixed Points in Partially Ordered Metric Spaces and Application. Nonlinear Analysis: Theory, Methods and Applications, 74, 983-992.
https://doi.org/10.1016/j.na.2010.09.055
[8] Beg, I. and Butt, A.R. (2010) Coupled Fixed Points of Set Valued Mappings in Partially Ordered Metric Spaces. Journal of Nonlinear Sciences and Applications, 3, 179-185.
https://doi.org/10.22436/jnsa.003.03.03
[9] Berinde, V. (2012) Coupled Fixed Point Theorems for φ-Contractive Mixed Monotone Map- pings in Partially Ordered Metric Spaces. Nonlinear Analysis: Theory, Methods and Applica- tions, 75, 3218-3228.
https://doi.org/10.1016/j.na.2011.12.021
[10] Samet, B. and Vetro, C. (2011) Coupled Fixed Point Theorems for Multi-Valued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces. Nonlinear Analysis: Theory, Meth- ods and Applications, 74, 4260-4268.
https://doi.org/10.1016/j.na.2011.04.007
[11] Malhotra, N. and Bansal, B. (2015) Some Common Coupled Fixed Point Theorems for Gen- eralized Contraction in b-Metric Spaces. Journal of Nonlinear Sciences and Applications, 8, 8-16.
https://doi.org/10.22436/jnsa.008.01.02
[12] Huang, L. and Zhang, X. (2007) Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings. Journal of Mathematical Analysis and Applications, 332, 1468-1476.
https://doi.org/10.1016/j.jmaa.2005.03.087
[13] Gupta, V., Shatanawi, W. and Kanwar, A. (2020) Coupled Fixed Point Theorems Employing CLR-Property on V-Fuzzy Metric Spaces. Mathematics, 8, 404.
https://doi.org/10.3390/math8030404
[14] Chen, J. and Huang, X. (2015) Coupled Fixed Point Theorems for Compatible Mappings in Partially Ordered G-Metric Spaces. Journal of Nonlinear Sciences and Applications, 8, 130- 141.
https://doi.org/10.22436/jnsa.008.02.05
[15] Hussain, N., Salimi, P. and Al-Mezel, S. (2013) Coupled Fixed Point Results on Quasi-Banach Spaces with Application to a System of Integral Equations. Fixed Point Theory and Applica- tions, 2013, Article No. 261.
https://doi.org/10.1186/1687-1812-2013-261
[16] Xin, Q.L. and Jiang, L.N. (2014) Fixed-Point Theorems for Mappings Satisfying the Or- dered Contractive Condition on Noncommutative Spaces. Fixed Point Theory and Applica- tions, 2014, Article No. 30.
https://doi.org/10.1186/1687-1812-2014-30
[17] Abbas, M., Khan, M.A. and Radenovic, S. (2010) Common Coupled Fixed Point Theorems in Cone Metric Spaces for w-Compatible Mappings. Applied Mathematics and Computation, 217, 195-202.
https://doi.org/10.1016/j.amc.2010.05.042
[18] Karapinar, E. (2010) Couple Fixed Point Theorems for Nonlinear Contractions in Cone Metric Spaces. Computers and Mathematics with Applications, 59, 3656-3668.
https://doi.org/10.1016/j.camwa.2010.03.062
[19] Sabetghadam, F., Masiha, H.P. and Sanatpour, A.H. (2009) Some Coupled Fixed Point Theo- rems in Cone Metric Spaces. Fixed Point Theory and Applications, 2009, Article No. 125426.
https://doi.org/10.1155/2009/125426
[20] Ma, Z.H., Jiang, L.N. and Sun, H.K. (2014) C∗-Algebra-Valued Metric Spaces and Related Fixed Point Theorems. Fixed Point Theory and Applications, 2014, Article No. 206.
https://doi.org/10.1186/1687-1812-2014-206
[21] Murphy, G.J. (1990) C∗-Algebras and Operator Theory. Academic Press, London.

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