Browse > Article
http://dx.doi.org/10.7858/eamj.2010.26.1.039

COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE  

Nashine, Hemant Kumar (DEPARTMENT OF MATHEMATICS DISHA INSTITUTE OF MANAGEMENT AND TECHNOLOGY)
Kim, Jong-Kyu (DEPARTMENT MATHEMATICS EDUCATION KYUNGNAM UNIVERSITY)
Publication Information
East Asian mathematical journal / v.26, no.1, 2010 , pp. 39-47 More about this Journal
Abstract
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.
Keywords
Best approximation; weakly compatible maps; subcompatible maps; convex metric space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. L. Hicks and M. D. Humpheries, A note on fixed point theorems, J. Approx. Theory 34 (1982), 221-225.   DOI
2 N. Shahzad, Invariant approximations, generalized I-contractions, and R-subweakly commuting maps, Fixed point theory and its Application 1 (2005), 79-86.
3 S. P. Singh, An application of a fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90.   DOI
4 S. P. Singh, Application of fixed point theorems to approximation theory, in: V. Lakshmikantam(Ed.), Applied nonlinear Analysis, Academic Press, New York, 1979.
5 S. P. Singh, B. Watson and P. Srivastava, Fixed point theory and best approximation:The KKM-Map Principle, Vol. 424, Kluwer Academic Publishers, 1997.
6 M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85(3) (1996), 318-323.   DOI   ScienceOn
7 I. Beg, N. Shahzad and M. Iqbal, Fixed point theorems and best approximation in convex metric space, J. Approx. Appl., 8(4) (1992), 97-105.
8 B. Brosowski, Fixpunktsatze in der Approximationstheorie, Mathematica (Cluj) 11 (1969), 165-220.
9 G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9(4) (1986), 771-779.   DOI   ScienceOn
10 G. Jungck and N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl., 325 (2007), 1003-1012.   DOI   ScienceOn
11 L. S. Liu, Common fixed point theorems for (sub) compatible and set valued generalized nonexpansive mappings in convex metric spaces, Appl. Math. Mech., 14(7) (1993),685-692.   DOI   ScienceOn
12 G. Meinardus, Invarianze bei linearen approximationen, Arch. Rational Mech. Anal.,14 (1963), 301-303.   DOI
13 S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx.Theory 55 (1988), 349-351.   DOI
14 N. Shahzad, Invariant approximations and R-subweakly commuting maps, J. Math.Anal. Appl., 257 (2001), 39-44.
15 P. V. Subrahmanyam, An application of a fixed point theorem to best approximations,J. Approx. Theory 20 (1977), 165-172.   DOI
16 W. Takahashi, A convexity in Metric sapce and nonexpansive mappings, Kodai Math.Sem. Rep., 22 (1970) 142-149.   DOI
17 L. S. Liu, On common fixed points of single valued mappings and setvalued mappings, J. Qufu Norm. Univ. Nat Sci. Ed., 18(1) (1992), 6-10.