Fixed points of multiplicative contraction mappings on multiplicative metric spaces

Yıl 2017, Cilt: 2 Sayı: 2, 65 - 79, 09.10.2017

Muttalip Özavşar

https://doi.org/10.30931/jetas.338608

Cited By: 6

Öz

In this paper, we first discussed multiplicative metric mapping by giving some
topological properties of the relevant multiplicative metric space. As an interesting result
of our discussions, we observed that the set of positive real numbers R_+ is a complete
multiplicative metric space with respect to the multiplicative absolute value function.
Furthermore, we introduced concept of multiplicative contraction mapping and proved
some fixed point theorems of such mappings on complete multiplicative metric spaces.

Anahtar Kelimeler

Multiplicative metric space, Fixed Point, Contractive Mapping

Kaynakça

• Bashirov, A.E., Kurpınar, E.M. and Ozyapıcı, A. Multiplicative calculus and its applications. J. Math.Analy. App. 337 (2008): 36-48.
• Jung Soon-Mo. A Fixed Point Approach to the Stability of Differential Equations y'=F(x,y). Bull of the Malys. Math.Sci. Soc. 33 (2010): 47-56.
• Kimura, Y. and Takahashi, W. Weak convergence to common fixed points of countable nonexpansive mappings and its applications. Journal of the Korean Mathematical Society 38 (2001): 1275-1284.
• Takahashi, W. Nonlinear Functional Analysis: Fixed point theory and its applications. Yokohama Publishers, 2000.