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FIXED POINTS OF CONVERSE COMMUTING MAPPINGS USING AN IMPLICIT RELATION
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 2,  2013, pp.109-117
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.2.109
 Title & Authors
FIXED POINTS OF CONVERSE COMMUTING MAPPINGS USING AN IMPLICIT RELATION
Chauhan, Sunny; Khan, M. Alamgir; Sintunavarat, Wutiphol;
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 Abstract
In the present paper, we utilize the notion of converse commuting mappings due to L [On common fixed points for converse commuting self-maps on a metric spaces, Acta. Anal. Funct. Appl. 4(3) (2002), 226-228] and prove a common fixed point theorem in Menger space using an implicit relation. We also give an illustrative example to support our main result.
 Keywords
t-norm;Menger space;weakly compatible mappings;converse commuting mappings;implicit relation;fixed point;
 Language
English
 Cited by
1.
Common Fixed Point Theorems for Conversely Commuting Mappings Using Implicit Relations, Journal of Operators, 2013, 2013, 1  crossref(new windwow)
 References
1.
I. Altun and D. Turkoglu, Some fixed point theorems on fuzzy metric spaces with implicit relations, Commun. Korean Math. Soc. 23(1) (2008), 111-124. MR2380234 crossref(new window)

2.
S. Chauhan and B. D. Pant, Common fixed point theorem for weakly compatible mappings in Menger space, J. Adv. Res. Pure Math. 3(2) (2011), 107-119. MR2800793 crossref(new window)

3.
B. S. Choudhury and K. P. Das, A new contraction principle in Menger spaces, Acta Math. Sinica (English Series) 24(8) (2008), 1379-1386. MR2438308 (2009f:54053) crossref(new window)

4.
B. S. Choudhury and K. P. Das, A coincidence point result in Menger spaces using a control function, Chaos, Solitons & Fractals 42(5) (2009), 3058-3063. MR2560014 (2010j:54062) crossref(new window)

5.
R. Chugh, Sumitra and M. A. Khan, Common fixed point theorems for converse commuting maps in fuzzy metric spaces, Internat. Math. Forum 6(37) (2011), 1845-1851.

6.
J.-x. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal. 71(5-6) (2009), 1833-1843. MR2524396 (2010g:54045) crossref(new window)

7.
J.-x. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal. 70(1) (2009), 184-193. MR2468228 (2009k:47164) crossref(new window)

8.
M. Imdad, J. Ali and M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons & Fractals 42(5) (2009), 3121-3129. MR2562820 (2010j:54064) crossref(new window)

9.
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9(4) (1986), 771-779. MR0870534 (87m:54122) crossref(new window)

10.
G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29(3) (1998), 227-238. MR1617919

11.
S. Kumar and B. Fisher, A common fixed point theorem in fuzzy metric space using property (E.A.) and implicit relation, Thai J. Math. 8(3) (2010), 439-446. MR2763666 (2011m:54045)

12.
S. Kumar and B. D. Pant, Common fixed point theorems in probabilistic metric spaces using implicit relation and property (E.A), Bull. Allahabad Math. Soc. 25(2) (2010), 223-235. MR2779240

13.
Z. Lu, Common fixed points for converse commuting selfmaps on a metric space, Acta Anal. Funct. Appl. (Chinese) 4(3) (2002), 226-228. MR1956719

14.
Q.-k. Liu and X.-q. Hu, Some new common fixed point theorems for converse commuting multi-valued mappings in symmetric spaces with applications, Nonlinear Anal. Forum 10(1) (2005), 97-104. MR2162343 (2006d:47102)

15.
K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535-537. crossref(new window)

16.
D. Mihet, A note on a common fixed point theorem in probabilistic metric spaces, Acta Math. Hungar. 125(1-2) (2009), 127-130. MR2564425 crossref(new window)

17.
S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japonica 36(2) (1991), 283-289. MR1095742

18.
B. D. Pant and S. Chauhan, A contraction theorem in Menger space, Tamkang J. Math. 42(1) (2011), 59-68. MR2815806

19.
B. D. Pant and S. Chauhan, Common fixed point theorems for two pairs of weakly compatible mappings in Menger spaces and fuzzy metric spaces, Sci. Stud. Res. Ser. Math. Inform. 21(2) (2011), 81-96. MR2956670

20.
B. D. Pant, S. Chauhan and Q. Alam, Common fixed point theorem in probabilistic metric space, Kragujevac J. Math. 35(3) (2011), 463-470. MR2881141

21.
H. K. Pathak and R. K. Verma, Integral type contractive condition for converse commuting mappings, Internat. J. Math. Anal. (Ruse) 3(24) (2009), 1183-1190. MR2604358

22.
H. K. Pathak and R. K. Verma, An integral type implicit relation for converse commuting maps, Internat. J. Math. Anal. (Ruse) 3(24) (2009), 1191-1198. MR2604359

23.
V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32(1) (1999), 157-163. MR1691726

24.
V. Popa and D. Turkoglu, Some fixed point theorems for hybrid contractions satisfying an implicit relation, Stud. Cercet. Stint. Ser. Math. Univ. Bacau (1998), no. 8, 75-86. MR1993808

25.
R. Saadati, D. O'Regan, S. M. Vaezpour and J. K. Kim, Generalized distance and common fixed point theorems in Menger probabilistic metric spaces, Bull. Iranian Math. Soc. 35(2) (2009), 97-117. MR2642929

26.
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. MR0115153 (22 #5955) crossref(new window)

27.
S. Sharma and B. Deshpande, On compatible mappings satisfying an implicit relation in common fixed point consideration, Tamkang J. Math. 33(3) (2002), 245-252. MR1923113 (2003f:47098)