Fixed points for non-self mappings in multiplicative metric spaces

Santosh Kumar; Terentius Rugumisa

doi:10.26637/MJM0604/0015

Abstract

In this paper, we develop a theorem for a pair of non-self mappings. For this purpose, we define a multiplicative convex metric space and state the condition for a mapping in such space to have a fixed point. We explain the procedure of locating the fixed point. We also provide an illustrative example on the use of the theorem.

Keywords:

Multiplicative metric space, non-self mapping, coincidence point, multiplicative convex set.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Santosh Kumar Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania. https://orcid.org/0000-0003-2121-6428
Terentius Rugumisa Faculty of Science, Technology and Environmental Studies, The Open University of Tanzania, Tanzania.

Pages: 800-806
Date Published: 01-10-2018
Vol. 6 No. 04 (2018): Malaya Journal of Matematik (MJM)

M. Abbas, B. Ali and Y. Suleiman, Common fixed points of locally contractive mappings in multiplicative metric spaces with application, International Journal of Mathematics and Mathematical Sciences, Vol. 2015 (2015), Article ID 218683, 7 pages.

N. Assad and W. Kirk, Fixed point theorems for setvalued mappings of contractive type, Pacific J. Math., $43(1972), 553-562$.

A. E. Bashirov, E. M. Kurplnara and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337(2008), 36-48.

L. Florack and H. V. Assen, Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision 42(1) (2012), 64-75.

M. Grossman and R. Katz, Non-Newtonian Calculus, Pigeon Cove, Lee Press, Massachusats, 1972.

X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed point Theory Appl., 2014(2014), Article ID 48.

Y. Jiang and F. Gu, Common coupled fixed point results in multiplicative metric spaces and applications, J. Nonlinear Sci. Appl., 10 (2017), 1881-1895

Q. H. Khan and M. Imdad, Coincidence and common fixed point theorems in a multiplicative metric spaces, Adv. Fixed Point Theory, 6(1)(2016), 1-9.

${ }^{[9]}$ M. Özavşar and A. C. Çevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, arXiv, 2012 (2012), 14 pages.

T. Rugumisa and Santosh Kumar, Unique common fixed points for pairs of multivalued mappings in partial metric spaces, Adv. Fixed Point Theory, 7(3)(2017), 391-412.