IJESM Volume 2, Issue 4 ISSN: 2320-0294
_________________________________________________________
A Quarterly Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories
Indexed & Listed at: Ulrich's Periodicals Directory ©, U.S.A., Open J-Gage, India as well as in Cabell’s Directories of Publishing Opportunities, U.S.A.
International Journal of Engineering, Science and Mathematics
http://www.ijmra.us
154
October
2013
December
2013
A Common Fixed point Theorem for Six Self
Mapping Under S-B property
Dr.V. K. Gupta
Swati Choursiya
Dr. V. H. Badshah
Abstract
In this paper we use the S-B property with semi compatibility, weakly compatibility and prove
common fixed point theorem for six self mapping on a fuzzy metric space.
Keywords- Weakly compatible, semi compatible, (S-B) property, Fuzzy metric space
Zadeh [15] was the foundation of fuzzy sets in 1965. To use this concept in topology and
analysis, many authors have extensively developed the theory of fuzzy sets and its applications.
Especially, Deng [2], Erceg [3], and Kramosil and Michalek [8] have introduced the concepts of
fuzzy metric spaces in different ways. In 1988, Grabiec [7] extended the fixed point theorem in
fuzzy metric space. George and Veeramani [5], [6] have modified the concept of fuzzy metric
space introduced by Kramosil and Michalek. They have also shown that every metric induces a
fuzzy metric. Singh et al. [14] proved various fixed point theorems using the concepts of semi-
compatibility, compatibility in Fuzzy metric space.
In this paper, we proved common fixed point theorem for six self mapping by using the
semi compatibility, weakly compatibility and new (S-B) property in fuzzy metric space, and
using the result from [9] and [11]
Govt. Madhav Science PG College, Vikram University, Ujjain (M.P), India
School of Studies in Mathematics, Vikram University, Ujjain, (M.P), India
Prof. and Head, School of Studies in Mathematics, Vikram University, Ujjain, (M.P) , India