DOI QR코드

DOI QR Code

COMMON FIXED POINT THEOREM AND INVARIANT APPROXIMATION IN COMPLETE LINEAR METRIC SPACES

  • Received : 2010.05.18
  • Accepted : 2000.08.22
  • Published : 2012.11.30

Abstract

A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

Keywords

References

  1. F. Akbar and A. R. Khan, Common fixed point and approximation results for non-commuting maps on locally convex spaces, Fixed Point Theory and Applications 2009, Article ID 207503, 14 pages, 2009.
  2. M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85 (1996), no. 3, 318-323. https://doi.org/10.1006/jath.1996.0045
  3. B. Brosowski, Fixpunktsatze in der Approximationstheorie, Mathematica (Cluj) 11 (1969), 165-220.
  4. W. G. Dotson, Fixed point theorems for nonexpasive mappings on starshaped subsets of Banach space, J. London Math. Soc. 4 (1972), no. 2 408-410.
  5. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
  6. G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13(1990), 497-500. https://doi.org/10.1155/S0161171290000710
  7. G. Jungck and B. E. Rhoades, Some fixed point theorem for compatible maps, Internat. J. Math. Math. Sci. 16 (1993), no. 3, 417-428. https://doi.org/10.1155/S0161171293000535
  8. G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2007), 1003-1012. https://doi.org/10.1016/j.jmaa.2006.02.058
  9. A. R. Khan, F. Akbar and N. Sultana, Random coincidence points of subcompatible multivalued maps with applications, Carpathian Journal of Mathematics 24 (2008), no. 2, 63-71.
  10. G. Meinardus, Invarianze bei linearen approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303. https://doi.org/10.1007/BF00250708
  11. H. K. Nashine and M. Imdad, Common fixed point and invariant approximations for subcompatible mappings in convex metric spaces, Math. Commun. 16 (2011), 1-12.
  12. H. K. Nashine and M. S. Khan, An application of fixed point theorem to best approximation in locally convex space, Appl. Math. Lett. 23 (2010), 121-127. https://doi.org/10.1016/j.aml.2009.06.025
  13. S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351. https://doi.org/10.1016/0021-9045(88)90101-3
  14. S. P. Singh, An application of a fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90. https://doi.org/10.1016/0021-9045(79)90036-4
  15. S. P. Singh, Application of fixed point theorems to approximation theory, in: V. Lakshmikantam(Ed.), Applied nonlinear Analysis, Academic Press, New York, 1979.
  16. S. P. Singh, Some results on best approximation in locally convex spaces, J. Approx. Theory 28 (1980), 329-332. https://doi.org/10.1016/0021-9045(80)90067-2