JOURNAL BROWSE
Search
Advanced SearchSearch Tips
COMMON FIXED POINTS UNDER LIPSCHITZ TYPE CONDITION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
COMMON FIXED POINTS UNDER LIPSCHITZ TYPE CONDITION
Pant, Vyomesh;
  PDF(new window)
 Abstract
The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.
 Keywords
Lipschitz type mapping pairs;nonexpansive conditions;noncompatible mappings;pointwise R-weak commutativity;R-weak commutativity of type ;contractive conditions;property (E.A);
 Language
English
 Cited by
1.
PROVING UNIFIED COMMON FIXED POINT THEOREMS VIA COMMON PROPERTY (E-A) IN SYMMETRIC SPACES,;;;

대한수학회논문집, 2010. vol.25. 4, pp.629-645 crossref(new window)
1.
Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property, International Journal of Mathematics and Mathematical Sciences, 2013, 2013, 1  crossref(new windwow)
2.
Common fixed points of (ψ,ϕ)-type contractive maps, Applied Mathematics Letters, 2012, 25, 6, 959  crossref(new windwow)
 References
1.
M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), no. 1, 181-188 crossref(new window)

2.
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779 crossref(new window)

3.
H. K. Pathak, Y. J. Cho, and S. M. Kang, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc. 34 (1997), no. 2, 247-257

4.
R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436-440 crossref(new window)

5.
R. P. Pant, R-weak commutativity and common fixed points of noncompatible maps, Ganita 49 (1998), no. 1, 19-27

6.
R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), no. 1, 251-258 crossref(new window)

7.
R. P. Pant, Common fixed points of Lipschitz type mapping pairs, J. Math. Anal. Appl. 240 (1999), no. 1, 280-283 crossref(new window)

8.
R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), no. 1, 284-289 crossref(new window)

9.
R. P. Pant, R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), no. 1, 37-42

10.
R. P. Pant and V. Pant, Lipschitz type condition and common fixed points, J. Indian Math. Soc. (N.S.) 67 (2000), no. 1-4, 179-182

11.
B. E. Rhoades, Contractive definitions and continuity, Fixed point theory and its applications (Berkeley, CA, 1986), 233-245, Contemp. Math., 72, Amer. Math. Soc., Providence, RI, 1988