Compatible mappings of type ( β ) and weak compatibility in fuzzy metric spaces

Shobha Jain; Shishir Jain; Lal Bahadur Jain

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 2, page 151-164
  • ISSN: 0862-7959

Abstract

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The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type ( β ) and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics ( 2006 ) ] and Sharma [Fuzzy Sets and Systems ( 2002 ) ] . An example has been constructed in support of our main result. All the results presented in this paper are new.

How to cite

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Jain, Shobha, Jain, Shishir, and Jain, Lal Bahadur. "Compatible mappings of type $(\beta )$ and weak compatibility in fuzzy metric spaces." Mathematica Bohemica 134.2 (2009): 151-164. <http://eudml.org/doc/38082>.

@article{Jain2009,
abstract = {The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type $ ( \beta ) $ and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics $(2006)] $ and Sharma [Fuzzy Sets and Systems $(2002) ] $. An example has been constructed in support of our main result. All the results presented in this paper are new.},
author = {Jain, Shobha, Jain, Shishir, Jain, Lal Bahadur},
journal = {Mathematica Bohemica},
keywords = {fuzzy metric space; common fixed points; $t$-norm; compatible maps of type $ (\beta ) $; compatible maps of type $ (\alpha ) $; weak compatible maps; fuzzy metric space; common fixed points; -norm; compatible maps of type },
language = {eng},
number = {2},
pages = {151-164},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Compatible mappings of type $(\beta )$ and weak compatibility in fuzzy metric spaces},
url = {http://eudml.org/doc/38082},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Jain, Shobha
AU - Jain, Shishir
AU - Jain, Lal Bahadur
TI - Compatible mappings of type $(\beta )$ and weak compatibility in fuzzy metric spaces
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 2
SP - 151
EP - 164
AB - The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type $ ( \beta ) $ and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics $(2006)] $ and Sharma [Fuzzy Sets and Systems $(2002) ] $. An example has been constructed in support of our main result. All the results presented in this paper are new.
LA - eng
KW - fuzzy metric space; common fixed points; $t$-norm; compatible maps of type $ (\beta ) $; compatible maps of type $ (\alpha ) $; weak compatible maps; fuzzy metric space; common fixed points; -norm; compatible maps of type
UR - http://eudml.org/doc/38082
ER -

References

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  10. Sharma, S., 10.1016/S0165-0114(01)00112-9, Fuzzy Sets Syst. 127 (2002), 345-352. (2002) MR1899067DOI10.1016/S0165-0114(01)00112-9
  11. Singh, B., Chouhan, M. S., Common fixed point theorems in fuzzy metric space, Fuzzy Sets Syst. 115 (2000), 471-475. (2000) 
  12. Singh, B., Jain, S., Fixed point theorem for six self maps in fuzzy metric space, J. Fuzzy Math. 14 (2006), 231-243. (2006) MR2211701
  13. Vasuki, R., Common fixed points for R -weakly commuting maps in fuzzy metric space, Indian J. Pure Appl. Math. (1999), 419-423. (1999) MR1695690
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