Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

COMMON FIXED POINT AND INVARIANT APPROXIMATION RESULTS

  • Abbas, Mujahid (DEPARTMENT OF MATHEMATICS INDIANA UNIVERSITY) ;
  • Kim, Jong-Kyu (DEPARTMENT OF MATHEMATICS EDUCATION KYUNGNAM UNIVERSITY)
  • Published : 2007.08.31
Download PDF
⟨ Previous Next ⟩

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

References

  1. 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
  2. M. A. Al-Thagafi and N. Shahzad, Noncommuting selfmaps and invariant approximations, Nonlinear Anal. 64 (2006), no. 12, 2778-2786 https://doi.org/10.1016/j.na.2005.09.015
  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 https://doi.org/10.1016/j.jmaa.2006.01.024
  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 https://doi.org/10.1016/j.jmaa.2005.08.045
  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 https://doi.org/10.1155/S0161171286000935
  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 https://doi.org/10.1016/0362-546X(94)90116-3
  15. G. Meinardus, Invarianz bei linearen Approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303 https://doi.org/10.1007/BF00250708
  16. R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436-440 https://doi.org/10.1006/jmaa.1994.1437