Occasionally Weakly Compatible Mappings^{1}School of Studies in Mathematics, Vikram University, Ujjain  456010 (M.P.), India
^{2}Department of Mathematical Science and Computer Application, Bundelkhand University, Jhansi (U.P.), India
Turkish Journal of Analysis and Number Theory. 2015, 3(3), 7882
doi: 10.12691/tjant332
Copyright © 2015 Science and Education Publishing
Cite this paper: Amit Kumar Govery, Mamta Singh. Occasionally Weakly Compatible Mappings.
Turkish Journal of Analysis and Number Theory. 2015; 3(3):7882. doi: 10.12691/tjant332.
Correspondence to: Amit Kumar Govery, School of Studies in Mathematics, Vikram University, Ujjain  456010 (M.P.), India. Email:
amitgovery@gmail.comAbstract
In this paper, the concept of compatible maps of type (A) and occasionally weakly compatible maps in fuzzy metric space have been applied to prove common fixed point theorem. A fixed point theorem for six self maps has been established using the concept of compatible maps of type (A) and occasionally weakly compatible maps, which generalizes the result of Cho .
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References
[1]  George and P. Veeramani, On some results in Fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395399. 

[2]  Jain and B. Singh, A fixed point theorem for compatible mappings of type (A) in fuzzy metric space, Acta Ciencia Indica, Vol. XXXIII M, No. 2 (2007), 339346. 

[3]  Jain, M. Sharma and B. Singh, Fixed point theorem using compatibility of type (β) in Fuzzy metric space, Chh. J. Sci. & Tech., Vol. 3 & 4, (2006 2007), 5362. 

[4]  Jain, V.H. Badshah, S.K. Prasad, Fixed Point Theorem in Fuzzy Metric Space for SemiCompatible Mappings, Int. J. Res. Rev. Appl. Sci. 12 (2012), 523526. 

[5]  Jain, V.H. Badshah, S.K. Prasad, The Property (E.A.) and The Fixed Point Theorem in Fuzzy Metric, Int. J. Res. Rev. Appl. Sci. 12 (2012), 527530. 

Show More References
[6]  Sharma, A. Jain, S. Chaudhary, A note on absorbing mappings and fixed point theorems in fuzzy metric space, Int. J. Theoretical Appl. Sci. 4 (2012), 5257. 

[7]  Singh, A. Jain, A.K. Govery, Compatibility of type (β) and fixed point theorem in Fuzzy metric space, Appl. Math. Sci. 5 (2011), 517528. 

[8]  Singh, A. Jain, A.K. Govery, Compatibility of type (A) and fixed point theorem in Fuzzy metric space,Int. J. Contemp. Math. Sci. 6 (2011), 10071018. 

[9]  Singh and M.S. Chouhan, Common fixed points of compatible maps in Fuzzy metric spaces, Fuzzy sets and systems, 115 (2000), 471475. 

[10]  E.P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers. 

[11]  G. Jungck, P.P. Murthy and Y.J. Cho, Compatible mappings of type (A) and common fixed points, Math. Japonica, 38 (1993), 381390. 

[12]  I.Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11(1975), 336344. 

[13]  L. A. Zadeh, Fuzzy sets, Inform and control 89 (1965), 338353. 

[14]  M.A. AlThagafi, N.A. Shahzad, A note on occasionally weakly compatible maps, Int. J. Math. anal. 3(2009), 5558. 

[15]  M.A. Khan, Sumitra, Common fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces, Far East J. Math. Sci., 9 (2008), 285293. 

[16]  S.H., Cho, On common fixed point theorems in fuzzy metric spaces, J. Appl. Math. & Computing Vol. 20 (2006), No. 12, 523533. 

[17]  S.N. Mishra, N. Mishra and S.L. Singh, Common fixed point of maps in fuzzy metric space, Int. J. Math. Math. Sci. 17(1994), 253258. 

[18]  M. Grebiec, Fixed points in Fuzzy metric space, Fuzzy sets and systems, 27(1998), 385389. 

[19]  Y.J. Cho, Fixed point in Fuzzy metric space, J. Fuzzy Math. 5(1997), 949962. 

[20]  Y.J. Cho, H.K. Pathak, S.M. Kang and J.S. Jung, Common fixed points of compatible mappings of type (β) on fuzzy metric spaces, Fuzzy sets and systems, 93 (1998), 99111. 

Show Less References