A Fixed Point Theorem for Non-Self Mappings in Multiplicative Metric Spaces

Yıl 2020, Cilt: 8 Sayı: 1, 1 - 6, 15.04.2020

Terentius Rugumisa Santosh Kumar

Öz

In this paper, we define the concept of metrical convexity in the context of multiplicative metric spaces. Using this, we then prove a fixed point theorem for non-self mappings in multiplicative metric spaces. Furthermore, we give an illustrative case on the utilization of the hypothesis.

Anahtar Kelimeler

Multiplicative metric space, non-self mapping, Fixed Point, Multiplicative convex set

Kaynakça

• [1] M. Abbas, B. Ali, Y. Suleiman, Common fixed points of locally contractive mappings in multiplicative metric spaces with application, International Journal of Mathematics and Mathematical Sciences, Vol. 2015, Article ID 218683, 7 pages.
• [2] A. E. Bashirov, E. M. Kurplnara, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (2008), 36-48.
• [3] M. Grossman, R. Katz. Non-Newtonian Calculus, Pigeon Cove, Lee Press, Massachusats, 1972.
• [4] H. Hxiaoju , M. Song, D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space. Fixed Point Theory and Applications 2014, 2014:48.
• [5] M. ÖzavŞar, A. C. Çevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, arXiv, 2012 (2012), 14 pages.
• [6] N. Assad, W. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math., Vol. 43, 1972, pp. 553-562.
• [7] Q. H. Khan, M. Imdad, Coincidence and common fixed point theorems in a multiplicative metric spaces, Adv. Fixed Point Theory, 6 (2016), No. 1, 1-9.
• [8] T. Rugumisa, S. Kumar, Unique common fixed points for pairs of multivalued mappings in partial metric spaces, Adv. Fixed Point Theory, 7 (2017), No. 3, 391-412.
• [9] X. He, M. Song, D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed point Theory Appl. 2014 (2014), Article ID 48.