Browse > Article
http://dx.doi.org/10.4134/CKMS.2012.27.4.733

COINCIDENCE AND COMMON FIXED POINT THEOREMS FOR SINGLE-VALUED AND SET-VALUED MAPPINGS  

Pant, Badri Datt (Government Degree College)
Samet, Bessem (Departement de Mathematiques Universite de Tunis, Ecole Superieure des Sciences et Techniques de Tunis 5, Avenue Taha Hussein-Tunis)
Chauhan, Sunny (R. H. Government Postgraduate College)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.4, 2012 , pp. 733-743 More about this Journal
Abstract
In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15].
Keywords
triangle norm; Menger space; occasionally weakly compatible maps; fixed point;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005), no. 2, 439-448.   DOI   ScienceOn
2 M. Stojakovic, Coincidence point for multivalued mappings in probabilistic space, Math. Japon. 40 (1994), no. 2, 283-288.
3 C. Vetro, Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces, Int. J. Modern Math. 4 (2009), no. 3, 277-284.
4 S. Zhang, On the theory of probabilistic metric spaces with applications, Acta Math. Sinica (N.S.) 1 (1985), no. 4, 366-377.   DOI
5 S. Zhang, N. Huang, and S. Chuan, A set-valued Caristi's theorem in probabilistic metric spaces, Sichuan Daxue Xuebao 30 (1993), no. 1, 12-16.
6 T. Zikic-Dosenovic, A multivalued generalization of Hicks C-contraction, Fuzzy Sets and Systems 151 (2005), no. 3, 549-562.   DOI   ScienceOn
7 K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535-537.   DOI   ScienceOn
8 D. Mihet, Multivalued generalizations of probabilistic contractions, J. Math. Anal. Appl. 304 (2005), no. 2, 464-472.   DOI   ScienceOn
9 S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36 (1991), no. 2, 283-289.
10 D. O'Regan and R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008), no. 1, 86-93.   DOI   ScienceOn
11 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.
12 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 (2012), no. 1-4, 127-138.
13 E. Pap, O. Hadzic, and R. Mesiar A fixed point theorem in probabilistic metric spaces and an application, J. Math. Anal. Appl. 202 (1996), no. 2, 433-449.   DOI   ScienceOn
14 H. K. Pathak, Y. J. Cho, S. S. Chang, and S. M. Kang, Coincidence point theorems for multi-valued and single-valued mappings in Menger PM-spaces, Tamkang J. Math. 26 (1995), no. 4, 313-319.
15 K. P. R. Sastry, G. A. Naidu, P. V. S. Prasad, V. M. Latha, and 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. (Ruse) 4 (2010), no. 27, 1341-1348.
16 B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York, 1983.
17 Lj. B. Ciric, B. Samet, and C. Vetro, Common fixed point theorems for families of occasionally weakly compatible mappings, Math. Comput. Modelling 53 (2011), no. 5-6, 631-636.   DOI   ScienceOn
18 O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Mathematics and its Applications, 536. Kluwer Academic Publishers, Dordrecht, 2001.
19 O. Hadzic, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Mat. Vesnik 3(16)(31) (1979), no. 2, 125-133.
20 O. Hadzic and Z. Ovcin, Fixed point theorems in fuzzy metric and probabilistic metric spaces, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 24 (1994), no. 2, 197-209.
21 O. Hadzic and E. Pap, Probabilistic multi-valued contractions and decomposable measures, Operations for uncertainty modelling (Liptovsky Mikulas, 2002). Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 10(Suppl.) (2002), 59-74.   DOI   ScienceOn
22 O. Hadzic and E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Systems 127 (2002), no. 2, 333-344.   DOI   ScienceOn
23 G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), no. 4, 771-779.   DOI   ScienceOn
24 G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
25 G. Jungck and B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2006), no. 2, 287-296.
26 M. A. Khan and Sumitra, Common fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces, Far East J. Math. Sci. 41 (2010), no. 2, 285-293.
27 H. Chandra and A. Bhatt, Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, Int. J. Math. Anal. (Ruse) 3 (2009), no. 9-12, 563-570.
28 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), no. 1, 17-23.
29 A. Aliouche and V. Popa, General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math. 39 (2009), no. 1, 89-109.
30 M. A. Al-Thagafi and N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica (Engl. Ser.) 24 (2008), no. 5, 867-876.   DOI
31 G. V. R. Babu and G. N. Alemayehu, Common fixed point theorems for occasionally weakly compatible maps satisfying property (E.A) using an inequality involving quadratic terms, Appl. Math. Lett. 24 (2011), no. 6, 975-981.   DOI   ScienceOn
32 A. Bhatt, H. Chandra, and D. R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010), no. 1, 176-182.   DOI   ScienceOn
33 H. Bouhadjera, A. Djoudi, and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Surv. Math. Appl. 3 (2008), 177-182.
34 H. Bouhadjera, A. Djoudi, and B. Fisher, A unique common fixed point theorem for occasionally weakly compatible maps, Bull. Allahabad Math. Soc. 24 (2009), no. 1, 1-6.
35 H. Bouhadjera and C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible maps, Acta Math. Vietnam. 36 (2011), no. 1, 1-17.
36 J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251.   DOI
37 S. S. Chang, Y. J. Cho, S. M. Kang, and J. X. Fan, Common fixed point theorems for multi-valued mappings in Menger PM-spaces, Math. Japon. 40 (1994), no. 2, 289-293.
38 S. S. Chang, Fixed Point theory with applications, Chongqing Publishing House, Chongqing, 1984.
39 T.-H. Chang, Common fixed point theorems for multivalued mappings, Math. Japon. 41 (1995), no. 2, 311-320.
40 S. S. Chang, Y. J. Cho, and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., Huntington, New York, 2001.
41 S. Chauhan and S. Kumar, Fixed points of occasionally weakly compatible mappings in fuzzy metric spaces, Scientia Magna 7 (2011), no. 2, 22-31.
42 S. Chauhan, S. Kumar, and B. D. Pant, Common fixed point theorem for weakly compatible mappings in Menger space, J. Adv. Res. Pure Math. 3 (2011), no. 2, 107-119.   DOI
43 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 (2010), no. 1-4, 13-21.
44 C.-M. Chen and T.-H. Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15.
45 S. Chuan, Caristi type hybrid fixed point theorems in Menger probabilistic metric space, Appl. Math. Mech. (English Ed.) 18 (1997), no. 2, 201-209.   DOI   ScienceOn
46 Lj. B. Ciric, R. P. Agarwal, and B. Samet, Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory Appl. 56 (2011), 13 pages.
47 V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory 6 (1972), 97-102.   DOI
48 C. T. Aage and J. N. Salunke, On fixed point theorems in fuzzy metric spaces, Int. J. Open Probl. Comput. Sci. Math. 3 (2010), no. 2, 123-131.
49 M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), Art. ID 54101, 9 pp.
50 M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces, Panamer. Math. J 18 (2008), no. 1, 55-62.