JOURNAL BROWSE
Search
Advanced SearchSearch Tips
FIXED POINT THEOREMS IN MENGER SPACES USING AN IMPLICIT RELATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.551-564
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.551
 Title & Authors
FIXED POINT THEOREMS IN MENGER SPACES USING AN IMPLICIT RELATION
Chauhan, Sunny; Khan, M. Alamgir; Pant, B.D.;
  PDF(new window)
 Abstract
In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876] introduced the notion of occasionally weakly compatible mappings in metric spaces. In this paper, we prove some common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using an implicit relation. We also give an illustrative example to support our main result.
 Keywords
t-norm;Menger space;occasionally weakly compatible mappings;implicit relation;fixed point;
 Language
English
 Cited by
 References
1.
C. T. Aage and J. N. Salunke, On fixed point theorems in fuzzy metric spaces, Int. J. Open Problems Compt. Math., 3(2) (2010), 123-131.

2.
M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occaionally weakly compatible mappings satisfying generalized contractive condition of integral type, Fixed point Theory and Applications, (2007), Article ID 54101, 9 pages.

3.
M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings dened on symmetric spaces, PanAmerican Math. J., 18(1) (2008), 55-62.

4.
M. Abbas and B. E. Rhoades, Common xed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition, Math. Comm., 13 (2008), 295-301.

5.
A. Aliouche and V. Popa, Common fixed point theorems for occasionally weakly compatible mappings via implicit relations, Filomat, 22(2) (2008), 99-107. crossref(new window)

6.
A. Aliouche and V. Popa, General common xed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math., 39(1) (2009), 89-109.

7.
M. A. Al-Thaga, N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876. crossref(new window)

8.
M. A. Al-Thaga, N. Shahzad, A note on occasionally weakly compatible maps, Int. J. Math. Anal., 3(2) (2009), 55-58.

9.
I. Altun, H. A. Hancer and D. Turkoglu, A fixed point theorem for multi-maps satisfying an implicit relation on metrically convex metric spaces, Math. Commun., 11 (2006), 17-23.

10.
A. Bhatt, H. Chandra and D. R. Sahu, Common xed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Analysis, 73 (2010), 176-182. crossref(new window)

11.
H. Bouhadjera, A general common fixed point theorem for occasionally weakly compatible maps., An. Univ. Oradea, Fasc. Mat., 17(2) (2010), 17-22.

12.
H. Bouhadjera and A. Djoudi, Common fixed point theorems of Gregus type for occasionally weakly compatible maps satisfying contractive conditions of integral type., An. Univ. Oradea, Fasc. Mat., 16 (2009), 145-152.

13.
H. Bouhadjera, A. Djoudi and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Surveys in Mathematics and its Applications, 3 (2008), 177-182.

14.
H. Bouhadjera, A. Djoudi and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Bull. Allahabad Math. Soc., 24(1) (2009), 1-6.

15.
H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible single and set-valued maps, HAL-00273238, Version 1, 15 April 2008.

16.
H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible maps, arXiv: 0812.3734v2 [math. FA], 17 June 2009.

17.
H. Chandra, A. Bhatt, Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, Int. J. Math. Anal., 3(12) (2009), 563-570.

18.
S. S. Chang, Y. J. Cho, S. M. Kang, Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan Univ. Press (Chengdu), 1994.

19.
S. S. Chang, Y. J. Cho, S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001.

20.
S. Chauhan and S. Kumar, Fixed point theorems in Menger spaces and applications to metric spaces, J. Appl. Math. Inform., 30(5-6) (2012), 729-740.

21.
S. Chauhan, S. Kumar and B. D. Pant, Common xed point theorems for occasionally weakly compatible mappings in Menger spaces, J. Adv. Research Pure Math., 3(4) (2011), 17-23.

22.
S. Chauhan and B. D. Pant, Common fixed point theorems for occasionally weakly compatible mappings using implicit relation, J. Indian Math. Soc. (N.S.), 77(1-4) (2010), 13-21.

23.
Lj. B. Ciric, B. Samet and C. Vetro, Common fixed point theorems for families of occasionally weakly compatible mappings, Math. Comp. Model., 53 (2011), 631-636. crossref(new window)

24.
O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Dordrecht: Kluwer Academic publishers, 2001.

25.
M. Imdad, S. Kumar and M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Rad. Math., 11 (2002), 135-143.

26.
G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998), 227-238.

27.
G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 7 (2006), 286-296.

28.
G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 9 (2008), 383-384. (Erratum)

29.
M. A. Khan and Sumitra, Common fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces, Far East J. Math. Sci., 41(2) (2009), 285-293.

30.
K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A., 28 (1942), 535-537. crossref(new window)

31.
S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japon., 36 (1991), 283-289.

32.
B. D. Pant, M. Abbas and S. Chauhan, Coincidences and common fixed points of weakly compatible mappings in Menger spaces, J. Indian Math. Soc. (N.S.), 80(1-4) (2013), 127-139.

33.
B. D. Pant and S. Chauhan, Common fixed point theorem for occasionally weakly compatible mappings in Menger space, Surv. Math. Appl., 6 (2011), 1-7.

34.
B. D. Pant and S. Chauhan, Fixed points of occasionally weakly compatible mappings using implicit relation, Commun. Korean Math. Soc., 27(3) (2012), 513-522. crossref(new window)

35.
B. D. Pant and S. Chauhan, Fixed point theorems for occasionally weakly compatible mappings in Menger spaces, Mat. Vesnik, 64(4) (2012), 267-274.]

36.
B. D. Pant, S. Chauhan and B. Fisher, Fixed point theorems for families of occasionally weakly compatible mappings, J. Indian Math. Soc. (N.S.), 79(1-4) (2012), 127-138.

37.
V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonsratio Math., 32 (1999), 157-163.

38.
V. Popa, A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonsratio Math., 33 (2000), 159-164.

39.
K. P. R. Sastry, G. A. Naidu, P. V. S. Prasad, V. M. Latha, S. S. A. Sastry, A critical look at fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric spaces, Int. J. Math. Anal., 4(27) (2010), 1341-1348.

40.
B. Schweizer, A. Sklar, Statistical metric spaces, Pacic J. Math., 10 (1960), 313-334. crossref(new window)

41.
B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holland, New York, 1983.

42.
V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory, 6 (1972), 97-102. crossref(new window)

43.
S. Sedghi, K. P. R. Rao and N. Shobe, A general common xed point theorem for multi-maps satisfying an implicit relation on fuzzy metric spaces, Filomat, 22(1) (2008), 1-11.

44.
S. Sharma and B. Deshpande, On compatible mappings satisfying an implicit relation in common xed point consideration, Tamkang J. Math., 33 (2002), 245-252.

45.
B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301 (2005), 439-448. crossref(new window)

46.
C. Vetro, Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces, Int. J. Modern Math., 4(3) (2009), 277-284.