Normed proper quasilinear spaces
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Authors
Sümeyye Çakan
- Department of Mathematics, Inönü University, 44280, Malatya, Turkey.
Yılmaz Yılmaz
- Department of Mathematics, Inönü University, 44280, Malatya, Turkey.
Abstract
The fundamental deficiency in the theory of quasilinear spaces, introduced by Aseev [S. M. Aseev, Trudy Mat.
Inst. Steklov., 167 (1985), 25–52], is the lack of a satisfactory definition of linear dependence-independence
and basis notions. Perhaps, this is the most important obstacle in the progress of normed quasilinear
spaces. In this work, after giving the notions of quasilinear dependence-independence and basis presented
by Banazılı[H. K. Banazılı, M.Sc. Thesis, Malatya, Turkey (2014)] and Çakan [S. Çakan, Ph.D. Seminar,
Malatya, Turkey (2012)], we introduce the concepts of regular and singular dimension of a quasilinear space.
Also, we present a new notion namely "proper quasilinear spaces" and show that these two kind dimensions
are equivalent in proper quasilinear spaces. Moreover, we try to explore some properties of finite regular
and singular dimensional normed quasilinear spaces. We also obtain some results about the advantages of
features of proper quasilinear spaces.
Share and Cite
ISRP Style
Sümeyye Çakan, Yılmaz Yılmaz, Normed proper quasilinear spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 816--836
AMA Style
Çakan Sümeyye, Yılmaz Yılmaz, Normed proper quasilinear spaces. J. Nonlinear Sci. Appl. (2015); 8(5):816--836
Chicago/Turabian Style
Çakan, Sümeyye, Yılmaz, Yılmaz. "Normed proper quasilinear spaces." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 816--836
Keywords
- Quasilinear spaces
- Hausdorff metric
- regular dimension
- singular dimension
- floor of an element
- proper sets
- proper quasilinear spaces.
MSC
- 06B99
- 06F99
- 46A99
- 46B40
- 46B99
- 47H04
- 54F05
- 65G40
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