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Common fixed point and invariant approximation results

김종규|Mujahid Abbas
대한수학회 (The Korean Mathematical Society)|2007.08|대한수학회보 (Bulletin of the KMS)|제44권 제3호|pp. 537-545

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참고문헌

주제분류수학

초록

Abstract

Necessary conditions for the existence of common xed pointsfor noncommuting mappings satisfying generalized contractive conditionsin the setup of certain metrizable topological vector spaces are obtained.As applications, related results on best approximation are derived. Ourresults extend, generalize and unify various known results in the litera-ture.

참고문헌 (20)

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  3. I. Beg, "Approximation of xed points of uniformly R-subweakly commuting mappings", 324(2), pp.1105~1114 (2006)
  4. I. Beg, "Coincidence point and invariant approximation for mappingssatisfying generalized weak contractive condition", pp.1~7 (2006)
  5. I. Beg, "Convergence theorems of the iterative schemes inconvex metric spaces", 11(3), pp.421~436 (2006)
  6. R. Chugh, "Common xed points for weakly compatible maps", 111(2), pp.241~247 (2001)
  7. N. Hussain, "Common xed point and invariant approximation results fornoncommuting generalized (f;g)-nonexpansive maps", 321(2), pp.851~861 (2006)
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  9. Amer, "Common xed points for commuting and compatible maps on compacta" (1988)
  10. G. Jungck, "Common xed points for noncontinuous nonself maps on nonmetric spaces", 4(2), pp.199~215 (1996)
  11. L. A. Khan, "An extension of Brosowski-Meinardus theorem on invariantapproximation", 11(4), pp.1~5 (1995)
  12. Kothe, "Translated from the German by D", Band 159 Springer-Verlag NewYork Inc
  13. "Fixed point theorems for asymptotically nonexpansive map-pings", (nlinear anal) (1994)
  14. "Invarianz bei linearen Approximationen" (1963)
  15. "Common xed points of noncommuting mappings" (1994)
  16. "International Series in Pure and AppliedMathematics" (1991), McGraw-Hill Inc
  17. "Invariant approximations, generalized I -contractions, and R-subweaklycommuting maps", (1), pp.79~86 (2005)
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  19. "On a weak commutativity condition of mappings in xed point considerations" (1982)
  20. "An application of a xed-point theorem to approximation theory", pp.~25 (1979)

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