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SETSCI - Volume 3 (2018)
ISAS2018-Winter - 2nd International Symposium on Innovative Approaches in Scientific Studies, Samsun, Turkey, Nov 30, 2018

Nurcan Bilgili Güngör1*
1Amasya University, Amasya, Turkey
* Corresponding author: bilgilinurcan@gmail.com
Published Date: 2019-01-14   |   Page (s): 310-312   |    10     3

ABSTRACT In 1964 Gahler introduced the theory of 2-normed spaces and then 1989 n-normed
spaces was first defined by Misiak. Then some researcher found new results on n-inner product
spaces and n-metric spaces. In 2001 Gunawan and Mashadi studied converges and completeness
in n-normed spaces and they gave a fixed point theorems for some n-Banach spaces. And in
2014 Kır and Kızıltunc defined phi-contraction map in n-Normed Spaces and proved fixed point
theorems which satisfy phi-contraction. On the other hand,in 1997 Alber and Guerre-Delabriere
defined weakly contractive maps and gave theorems in uniformly smooth and uniformly convex
Banach spaces. Then in 2001 Rhoades extended some theorems of their work to arbitrary
Banach spaces for weakly contractions. In this paper the notion of weakly contractive maps
on n-Normed spaces are presented. Also some fixed point theorems for weak contractive maps
are proved. Thus, we will provide a source for new studies related to weak contractions in
n-normed spaces.  
REFERENCES [1] Alber, Y. I.and Guerre-Delabriere, S., Principle of weakly contractive maps in Hilbert spaces. In New Results in Operator Theory and Its Applications, 1997 (pp. 7-22). Birkhuser, Basel.
[2] Ghler, S., Lineare 2-normierte Rume. Mathematische Nachrichten,1964 28(1-2), 1-43.
[3] Gunawan, H.and Mashadi, M., On n-normed spaces. International Journal of Mathematics and Mathematical Sciences, 27(10),2001, 631-639.
[4] Kır, M. and Kızıltunc, H., On fixed point theorems for contraction mappings in n-normed spaces. Appl. Math. Inf. Lett, 2,2014, 59-64.
[5] Misiak, A., n-inner product spaces. Mathematische Nachrichten, 140(1), 1989, 299-319.
[6] Rhoades, B. E., Some theorems on weakly contractive maps. Nonlinear Analysis, 4(47), 2001, 2683-2693.

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