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.  

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[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.