Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2018, 6(2), 52-56
DOI: 10.12691/tjant-6-2-4
Open AccessArticle

Fixed Point Theorems for Expansive Type Mappings in Multiplicative Metric Spaces

Nisha Sharma1, Lakshmi Narayan Mishra2, and Vishnu Narayan Mishra3

1Manav Rachna International Institute of Research and Studies, Faridabad 121 004, Haryana, India

2Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India

3Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak 484 887, Madhya Pradesh, India

Pub. Date: April 30, 2018

Cite this paper:
Nisha Sharma, Lakshmi Narayan Mishra and Vishnu Narayan Mishra. Fixed Point Theorems for Expansive Type Mappings in Multiplicative Metric Spaces. Turkish Journal of Analysis and Number Theory. 2018; 6(2):52-56. doi: 10.12691/tjant-6-2-4

Abstract

In this paper, we prove some common fixed point theorems for various types of compatible mappings in the setting of complete multiplicative metric spaces.

Keywords:
multiplicative metric space compatible mapping expansive mappings

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  A.E. Bashirov, E.M. Kurplnara, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (2008), 36-48.
 
[2]  M. Abbas, B. Ali, Y.I. Suleiman, Common fixed points of locally contractive mappings in multiplicative metric spaces with application, Int. J. Math. Sci., 2015(2015), Article ID 218683, 7 pages.
 
[3]  S.M. Kang, P. Kumar, S. Kumar, common fixed points for compatible mappings of types in multiplicative metric spaces, Int. J. Math. Anal., 9 (2015), 1755-1767.
 
[4]  X. He, M. Song, D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric spaces, Fixed Point Theory Appl., 48 (2014), 9 pages.
 
[5]  M. Ozavsar, A.C. Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, arXiv:1205.5131v1 [math.GM], 2012.
 
[6]  S.M. Kang, P. Kumar, S. Kumar, P. Nagpal, S.K. Garg, Common fixed points for compatible mappings and its variants in multiplicative metric spaces, Int. J. Pure Appl. Math., 102 (2015), 383-406.
 
[7]  S.Z. Wang, B.Y, Li, Z.M. Gao, K. Iseki, Some fixed point theorems on expansion mappings, Math. Japon., 29 (1984), 631-636.
 
[8]  B.E. Rhoades, An expansion mapping theorem, Jnanabha, 23 (1993), 151-152.
 
[9]  M. Sarwar, R. Badshah-e, Some unique fixed point theorems in multiplicative metric space, arXiv:1410.3384v2 [math.GM], 2014.
 
[10]  P.Z. Daffer, H. Kaneko, on expansive mappings, Math. Japonica, 37(1992), 733-735.