JOURNAL BROWSE
Search
Advanced SearchSearch Tips
EMPLOYING COMMON LIMIT RANGE PROPERTY WITH VARIANTS OF R-WEAKLY COMMUTING MAPPINGS IN METRIC SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : The Pure and Applied Mathematics
  • Volume 22, Issue 2,  2015, pp.127-138
  • Publisher : Korea Society of Mathematical Education
  • DOI : 10.7468/jksmeb.2015.22.2.127
 Title & Authors
EMPLOYING COMMON LIMIT RANGE PROPERTY WITH VARIANTS OF R-WEAKLY COMMUTING MAPPINGS IN METRIC SPACES
CHAUHAN, SUNNY; VUJAKOVIC, JELENA; HAQ, SHAMSUL;
  PDF(new window)
 Abstract
The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying -contractive condition.
 Keywords
metric space;R-weakly commuting mappings;R-weakly commuting mappings of type (Ag);R-weakly commuting mappings of type (Af );R-weakly commuting mappings of type (P);property (E.A);common limit range property;fixed point;
 Language
English
 Cited by
 References
1.
M. Aamri & D.El Moutawakil: Some new common fixed point theorems under strict contractive conditions. J. Math. Anal. Appl. 270(1) (2002), 181-188. MR1911759 (2003d:54057) crossref(new window)

2.
M. Abbas, T. Nazir & S. Radenović: Common fixed point of power contraction mappings satisfying (E.A) property in generalized metric spaces. Appl. Math. Comput. 219 (2013), 7663-7670. crossref(new window)

3.
M.A. Alghamdi, S. Radenović & N. Shahzad: On some generalizations of commuting mappings. Abstr. Appl. Anal. 2012, Article ID 952052.

4.
S. Banach: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3 (1922), 133-181.

5.
Lj.B. Ćirić: Generalized contractions and fixed point theorems. Publ. Inst. Math.(Beograd) (N.S.) 12 (1971), no. 26, 19-26. MR0309092 (46 #8203)

6.
D. Đorić, Z. Kadelburg & S. Radenović: A note on occasionally weakly compatible mappings and common fixed points. Fixed Point Theory 13 (2012), no. 2, 475-480.

7.
G. Jungck: Commuting mappings and fixed point. Amer. Math. Monthly 83 (1976), no. 4, 261-263. MR0400196 (53 #4031) crossref(new window)

8.
G. Jungck: Compatible mappings and common fixed points. Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. MR0870534 (87m:54122) crossref(new window)

9.
Z. Kadelburg, S. Radenović & B. Rosić: Strict contractive conditions and common fixed point theorems in cone metric spaces. Fixed Point Theory Appl. 2009, Article ID173838, 14 pages.

10.
Z. Kadelburg, S. Radenović & N. Shahzad: A note on various classes of compatible type pairs of mappings and common fixed point theorems. Abstr. Appl. Anal. 2013, ArticleID 697151, 6 pages.

11.
R. Kannan: Some results on fixed points. Bull. Calcutta Math. Soc. 60 (1968), 71-76. MR0257837 (41 #2486)

12.
S. Kumar: A note on Jungck’s fixed point theorem. Fasciculi Math. 45 (2010), 59-69.

13.
W. Long, M. Abbas, T. Nazir & S. Radenović: Common fixed point for two pairs of mappings satisfying (E.A) property in generalized metric spaces. Abstr. Appl. Anal. 2012, Article ID 394830, 15 pages.

14.
P.P. Murthy: Important tools and possible applications of metric fixed point theory. Proceedings of the ThirdWorld Congress of Nonlinear Analysts, Part 5 (Catania, 2000), Nonlinear Anal. 47 (2001), no. 5, 3479-3490. MR1979244 (2004d:54038) crossref(new window)

15.
R.P. Pant: Common fixed points of noncommuting mappings. J. Math. Anal. Appl. 188 (1994), no. 2, 436-440. MR1305460 (95j:54037) crossref(new window)

16.
R.P. Pant: Common fixed point theorems for contractive maps. J. Math. Anal. Appl. 226 (1998), no. 1, 251-258. MR1646430 (99h:54063) crossref(new window)

17.
R.P. Pant: Discontinuity and fixed points. J. Math. Anal. Appl. 240 (1999), no. 1, 280-289. MR1728194 (2000j:54048) crossref(new window)

18.
R.P. Pant: Noncompatible mappings and common fixed points. Soochow J. Math. 26 (2000), no. 1, 29-35. MR1755133 (2000m:54048)

19.
V. Pant: Contractive conditions and common fixed points. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 24 (2008), no. 2, 257-266. MR2461637 (2009h:54061)

20.
H.K. Pathak, Y.J. Cho & S.M. Kang: Remarks on R-weakly commuting mappings and common fixed point theorems. Bull. Korean Math. Soc. 34 (1997), no. 2, 247-257.

21.
S. Radenović, Z. Kadelburg, D. Jandrlić & A. Jandrlić: Some results on weakly contractive maps. Bull. Iran. Math. Soc. 38 (2012), no. 3, 625-645.

22.
K.P.R. Sastry & I.S.R. Krishna Murthy: Common fixed points of two partially commuting tangential selfmaps on a metric space. J. Math. Anal. Appl. 250 (2000), no. 2, 731-734. MR1786095 crossref(new window)

23.
S. Sessa: On a weak commutativity condition in fixed point considerations. Publ. Inst.Math. (Beograd) (N.S.) 32 (1982), no. 46, 149-153. MR0710984 (85f:54107)

24.
S.L. Singh & A. Kumar: Common fixed point theorems for contractive maps. Mat.Vesnik 58 (2006), no. 3-4, 85-90.

25.
S.L. Singh, B.D. Pant & S. Chauhan: Fixed point theorems in Non-Archimedean Menger PM-spaces. J. Nonlinear Anal. Optim. 3 (2012), no. 2, 153-160. MR2982403

26.
S.L. Singh & A. Tomar: Weaker forms of commuting maps and existence of fixed points. J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 10 (2003), no. 3, 145-161. MR2011365 (2004h:54039)

27.
W. Sintunavarat & P. Kumam: Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces. J. Appl. Math. Vol. 2011, Article ID637958, 14 pp. MR2822403

28.
W. Sintunavarat & P. Kumam: Common fixed points for R-weakly commuting in fuzzy metric spaces. Ann. Univ. Ferrara Sez. VII Sci. Mat. 58 (2012), no. 2, 389-406. crossref(new window)

29.
W. Sintunavarat & P. Kumam: Coincidence and common fixed points for hybrid strict contractions without weakly commuting condition. Appl. Math. Lett. 22 (2009), 1877-1881. crossref(new window)

30.
W. Sintunavarat, P. Kumam & P. Patthanangkoor: Common random fixed points for multivalued random operators without S and T-weakly commuting random. Random Oper. Stoch. Equ. 17 (2009), no. 4, 381-388.

31.
N. Wairojjana, W. Sintunavarat & P. Kumam: Common tripled fixed points for W-compatible mappings along with CLRg property in abstract metric spaces. J. Inequal.Appl. 2014, 2014:133. crossref(new window)