Research Article
Year 2020,
, 381 - 393, 10.01.2020
Abstract
In the realms of theoretical computer science and approximation theory, asymetric normed spaces play an important role. In this paper, by combining asymmetric norm and cone norm, it is defined asymmetric cone normed spaces. Also, it is introduced and studied some topological concepts in asymmetric cone normed spaces.
Keywords
References
- Long-Guang, H. and Xian, Z., Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476, (2007).
- Türkoğlu, D. and Abuloha, M., Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Mathematica Sinica, English Series, 26, 3, 489-496, (2010).
- Abdeljawad, T., Türkoğlu, D. and Abuloha, M., Some theorems and examples of cone Banach spaces, Journal of Computational Analysis and Applications, 12, 4, 739-753, (2010).
- Gordji, M. E., Ramezani, M. Khodaei H. and Baghani, H., Cone normed spaces, Caspian Journal of Mathematical Sciences, 1, 1, 7-12, (2012).
- Deimling, K., Nonlinear functional analysis, Springer-Verlag, Berlin, (1985).
- Radenovic, S. and Kadelburg, Z., Quasi-contractions on symmetric and cone symmetric spaces, Banach Journal of Mathematical Analysis, 5, 38-50, (2011).
- Wilson, W. A., On quasi metric spaces, American Journal of Mathematics, 53, 675-684, (1931).
- Garcia-Raffi, L. M., Compactness and finite dimension in asymmetric normed linear spaces, Topology and Its Applications, 153, 844-853, (2005).
- Alegre, C., Ferrando, I., Garcia-Raffi, L. M. And Sanchez Perez, E. A., Compactness in asymmetric normed spaces, Topology and Its Applications, 155, 6, 527-539, (2008).
- Cobzas, S., Functional analysis in asymmetric normed spaces, Birkhauser, (2012).
- Collins J. and Zimmer, J., An asymmetric Arzela Ascoli theorem, Topology and Its Applications, 154, 2312-2322, (2007).
- İlkhan, M., Zengin Alp, P. and Kara, E. E., On the spaces of linear operators acting between asymmetric cone normed spaces, Mediterranean Journal of Mathematics, 15, 136, 12 pages, (2018).
- Kelly, J. C., Bitopological spaces, Proceedings of the London Mathematical Society, 13, 1, 71-89, (1963).
- Reilly, I. L., Subrahmanyam, P. V. And Vamanamurthy, V. K., Cauchy sequences in quasi-pseudo-metric spaces, Monatshefte für Mathematik, 93, 127, 127-140, (1982).
- Romaguera, S., Left K-completeness in quasi metric spaces, Mathematische Nachrichten, 157, 15-23, (1992).
Year 2020,
, 381 - 393, 10.01.2020
Abstract
Teorik bilgisayar bilimi ve yaklaşım teorisi alanlarında asimetrik normlu uzaylar önemli bir rol oynamaktadır. Bu çalışmada asimetrik norm ve konik norm birleştirilerek asimetrik konik normlu uzaylar tanımlanmaktadır. Ayrıca asimetrik konik normlu uzaylarda bazı topolojik kavramlar tanıtılmakta ve çalışılmaktadır
Keywords
References
- Long-Guang, H. and Xian, Z., Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476, (2007).
- Türkoğlu, D. and Abuloha, M., Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Mathematica Sinica, English Series, 26, 3, 489-496, (2010).
- Abdeljawad, T., Türkoğlu, D. and Abuloha, M., Some theorems and examples of cone Banach spaces, Journal of Computational Analysis and Applications, 12, 4, 739-753, (2010).
- Gordji, M. E., Ramezani, M. Khodaei H. and Baghani, H., Cone normed spaces, Caspian Journal of Mathematical Sciences, 1, 1, 7-12, (2012).
- Deimling, K., Nonlinear functional analysis, Springer-Verlag, Berlin, (1985).
- Radenovic, S. and Kadelburg, Z., Quasi-contractions on symmetric and cone symmetric spaces, Banach Journal of Mathematical Analysis, 5, 38-50, (2011).
- Wilson, W. A., On quasi metric spaces, American Journal of Mathematics, 53, 675-684, (1931).
- Garcia-Raffi, L. M., Compactness and finite dimension in asymmetric normed linear spaces, Topology and Its Applications, 153, 844-853, (2005).
- Alegre, C., Ferrando, I., Garcia-Raffi, L. M. And Sanchez Perez, E. A., Compactness in asymmetric normed spaces, Topology and Its Applications, 155, 6, 527-539, (2008).
- Cobzas, S., Functional analysis in asymmetric normed spaces, Birkhauser, (2012).
- Collins J. and Zimmer, J., An asymmetric Arzela Ascoli theorem, Topology and Its Applications, 154, 2312-2322, (2007).
- İlkhan, M., Zengin Alp, P. and Kara, E. E., On the spaces of linear operators acting between asymmetric cone normed spaces, Mediterranean Journal of Mathematics, 15, 136, 12 pages, (2018).
- Kelly, J. C., Bitopological spaces, Proceedings of the London Mathematical Society, 13, 1, 71-89, (1963).
- Reilly, I. L., Subrahmanyam, P. V. And Vamanamurthy, V. K., Cauchy sequences in quasi-pseudo-metric spaces, Monatshefte für Mathematik, 93, 127, 127-140, (1982).
- Romaguera, S., Left K-completeness in quasi metric spaces, Mathematische Nachrichten, 157, 15-23, (1992).
There are 15 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | January 10, 2020 |
| Submission Date | September 24, 2019 |
| Published in Issue | Year 2020 |