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COMMON FIXED POINT AND INVARIANT APPROXIMATION RESULTS
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 Title & Authors
COMMON FIXED POINT AND INVARIANT APPROXIMATION RESULTS
Abbas, Mujahid; Kim, Jong-Kyu;
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 Abstract
Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.
 Keywords
metrizable topological vector space;common fixed point;uniformly R-subweakly commuting mapping;asymptotically S-nonexpansive mapping;best approximation;
 Language
English
 Cited by
 References
1.
M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85 (1996), no. 3, 318-323 crossref(new window)

2.
M. A. Al-Thagafi and N. Shahzad, Noncommuting selfmaps and invariant approximations, Nonlinear Anal. 64 (2006), no. 12, 2778-2786 crossref(new window)

3.
I. Beg, D. R. Sahu, and S. D. Diwan, Approximation of fixed points of uniformly R-subweakly commuting mappings, J. Math. Anal. Appl. 324 (2006), no. 2, 1105-1114 crossref(new window)

4.
I. Beg and M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory Appl. 2006, Art. ID 74503, 1-7

5.
I. Beg, M. Abbas, and J. K. Kim, Convergence theorems of the iterative schemes in convex metric spaces, Nonlinear Funct. Anal. Appl., 11 (2006), no. 3, 421-436

6.
R. Chugh and S. Kumar, Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. Math. Sci. 111 (2001), no. 2, 241-247

7.
N. Hussain and G. Jungck, Common fixed point and invariant approximation results for noncommuting generalized (f, g)-nonexpansive maps, J. Math. Anal. Appl. 321 (2006), no. 2, 851-861 crossref(new window)

8.
N. Hussain and B. E. Rhoades, $C_q$-commuting maps and invariant approximations, Fixed Point Theory Appl. 2006, Art. ID 24543, 1-9

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

10.
G. Jungck, Common ?xed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), no. 3, 977-983

11.
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4 (1996), no. 2, 199-215

12.
L. A. Khan and A. R. Khan, An extension of Brosowski-Meinardus theorem on invariant approximation, Approx. Theory Appl. (N.S.) 11 (1995), no. 4, 1-5

13.
G. KothAe, Topological vector spaces. I, Translated from the German by D. J. H. Garling. Die Grundlehren der mathematischen Wissenschaften, Band 159 Springer-Verlag New York Inc., New York 1969

14.
T.-C. Lim and H. K. Xu, Fixed point theorems for asymptotically nonexpansive mappings, Nonlinear Anal. 22 (1994), no. 11, 1345-1355 crossref(new window)

15.
G. Meinardus, Invarianz bei linearen Approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303 crossref(new window)

16.
R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436-440 crossref(new window)