Abstract
The concept of C^{∗}-algebra-valued rectangular b-metric spaces is introduced as a generalization of C^{∗}-algebra-valued b-metric spaces. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. As applications, existence and uniqueness results for a type of operator equation is given.
Keywords
C^{∗}-algebra; C^{∗}-algebra-valued rectangular b-metric spaces contractive mapping fixed point theorem
References
- Bai, C., Coupled fixed point theorems in C^{∗}-algebra-valued b-metric spaces with application, Fixed Point Theory and Appl, 70(2016).
- Batul, S. and Kamran, T., C^{∗}-valued contractive type mappings, Fixed Point Theory Appl., 142(2015).
- Branciari, A., A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen, 57(12),(2000) 31-37.
- Czerwik, S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46(2),(1998) 263-276.
- Erden, M. and Alaca, C., C^{∗}-algebra-valued S-metric spaces, Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics, 67(2),(2018) 165-177.
- George, R., Radenovic, S., Reshma, K.P. and Shukla, S., Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8,(2015) 1005-1013.
- Kamran, T., Postolache, M., Ghiura, A., Batul, S. and Ali, R., The Banach contraction principle in C^{∗}-algebra-valued b-metric spaces with application, Fixed Point Theory and Appl, 10(2016).
- Ma, ZH. Jiang, L. Hongkai, C^{∗}-algebra-valued metric spaces and related fixed point theorems: Fixed point Theory Appl., 206(2014).
- Ma, ZH. and Jiang, L., C^{∗}-algebra-valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl., 222(2015). Murphy, G.J., C^{∗}-Algebras and Operator Theory, Academic Press, London, 1990.
- Shehwar Dur, E., Batul, S., Kamran, T. and Ghiura, A., Caristia's fixed point theorem on C*-algebra valued metric spaces, J. Nonlinear Sci. Appl., 9,(2016) 584-588.
Abstract
References
- Bai, C., Coupled fixed point theorems in C^{∗}-algebra-valued b-metric spaces with application, Fixed Point Theory and Appl, 70(2016).
- Batul, S. and Kamran, T., C^{∗}-valued contractive type mappings, Fixed Point Theory Appl., 142(2015).
- Branciari, A., A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen, 57(12),(2000) 31-37.
- Czerwik, S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46(2),(1998) 263-276.
- Erden, M. and Alaca, C., C^{∗}-algebra-valued S-metric spaces, Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics, 67(2),(2018) 165-177.
- George, R., Radenovic, S., Reshma, K.P. and Shukla, S., Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8,(2015) 1005-1013.
- Kamran, T., Postolache, M., Ghiura, A., Batul, S. and Ali, R., The Banach contraction principle in C^{∗}-algebra-valued b-metric spaces with application, Fixed Point Theory and Appl, 10(2016).
- Ma, ZH. Jiang, L. Hongkai, C^{∗}-algebra-valued metric spaces and related fixed point theorems: Fixed point Theory Appl., 206(2014).
- Ma, ZH. and Jiang, L., C^{∗}-algebra-valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl., 222(2015). Murphy, G.J., C^{∗}-Algebras and Operator Theory, Academic Press, London, 1990.
- Shehwar Dur, E., Batul, S., Kamran, T. and Ghiura, A., Caristia's fixed point theorem on C*-algebra valued metric spaces, J. Nonlinear Sci. Appl., 9,(2016) 584-588.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Review Articles |
| Authors | |
| Publication Date | August 1, 2019 |
| Submission Date | February 5, 2018 |
| Acceptance Date | June 19, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
