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Best Approximations and Fixed Point Theorems

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Approximation Theory, Wavelets and Applications

Part of the book series: NATO Science Series ((ASIC,volume 454))

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Abstract

In this paper, a survey on best approximation and fixed points is presented. Severall fixed point theorems are de rived as corollaries.

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References

  1. Browder, F.E. Fixed point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci., USA 53 (1965) 1272–1276.

    Article  MathSciNet  Google Scholar 

  2. Browder, F.E. Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces, Arch. Rational Mech. Anal., 24 (1967) 82–90.

    Article  MathSciNet  MATH  Google Scholar 

  3. Browder, F.E. and Petryshyn, W.V. Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20 (1967) 197–228.

    Article  MathSciNet  MATH  Google Scholar 

  4. Carbone, A. Kakutani factorizable maps and best approximation, Indian J. Math (to appear).

    Google Scholar 

  5. Cheney, E.W. Introduction to approximation theory, McGraw-Hill Co. New York (1966).

    MATH  Google Scholar 

  6. Cheney, E.W. and Goldstein, A.A. Proximity Maps for convex sets, Proc. Amer. Math. Soc., 10 (1959) 448–450.

    Article  MathSciNet  MATH  Google Scholar 

  7. Fan, Ky. Extensions of two fixed point theorems of F.E. Browder, Math. Z., 112 (1969) 234–240.

    Article  MathSciNet  MATH  Google Scholar 

  8. Fan, Ky. Fixed point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. USA, 38 (1952) 121–126.

    Article  MATH  Google Scholar 

  9. Himmelberg, C.J. Fixed points of compact multifunctions, J. Math. Anal. Appl., 38 (1972) 205–207.

    Article  MathSciNet  Google Scholar 

  10. Lassonde, M. Fixed points for Kakutani factorizable multifunctions, J. Math. Anal. Appl., 152 (1990) 46–60.

    Article  MathSciNet  MATH  Google Scholar 

  11. Park, S. On generalizations of Ky Fan’s theorem on best approximation, Nurner. Funct. Anal. and Optimiz., 9 (1987) 619–628.

    Article  MATH  Google Scholar 

  12. Prolla, J.B. Fixed point theorems for set-valued mappings and existence of best approximants, Numer. Funct. Anal. and Optimiz., 5(4) (1982–83) 449–455.

    Article  MathSciNet  Google Scholar 

  13. Reich, S. Fixed points in locally convex spaces, Math. Z., 125 (1972) 17–32.

    Article  MathSciNet  MATH  Google Scholar 

  14. Reich, S. Approximate selections,best approximations, fixed points and invariant sets, J. Math Anal. Appl., 62 (1978) 104–113.

    Article  MathSciNet  MATH  Google Scholar 

  15. Reich, S. Fixed point theorems for set-valued mappings, J. Math Anal. Appl. 69 (1979) 353–358.

    Article  MathSciNet  MATH  Google Scholar 

  16. Schöneberg, R. Some fixed point theorems for mappings of nonexpansive type, Com. Math. Univ. Carolinae, 17 (1976) 399–411.

    MATH  Google Scholar 

  17. Sehgal, V.M. and Singh, S.P. A generalization to multifunctions of Fan’s best approximation theorem, Proc. Amer. Math. Soc., 102 (1988) 534–537.

    MathSciNet  MATH  Google Scholar 

  18. Sehgal, V.M. and Singh, S.P. A theorem on best approximation, Numer. Funct. Anal. and Optimiz., 10 (1989) 181–184.

    Article  MathSciNet  MATH  Google Scholar 

  19. Singh, S.P. and Watson, B. Proximity maps and fixed points, J. Approx. Theory, 39 (1983) 72–76.

    Article  MathSciNet  MATH  Google Scholar 

  20. Singh, S.P. and Watson, B. On approximating fixed points, Proc. Sym. Pure Math. Amer. Math. Soc., 45 (1986) 393–395.

    Article  MathSciNet  Google Scholar 

  21. Vetrivel, V., Veeramani, P. and Bhattacharyya, P. Some extensions of Fan’s best approximation theorem, Numer. Funct. Anal. and Optimiz., 13 (1992) 397–402.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NF, A1C 5S7, Canada

    S. P. Singh & B. Watson

Authors
  1. S. P. Singh
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  2. B. Watson
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Editor information

Editors and Affiliations

  1. Memorial University of Newfoundland, St. John’s, Newfoundland, Canada

    S. P. Singh

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© 1995 Springer Science+Business Media Dordrecht

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Singh, S.P., Watson, B. (1995). Best Approximations and Fixed Point Theorems. In: Singh, S.P. (eds) Approximation Theory, Wavelets and Applications. NATO Science Series, vol 454. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8577-4_15

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  • DOI: https://doi.org/10.1007/978-94-015-8577-4_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4516-4

  • Online ISBN: 978-94-015-8577-4

  • eBook Packages: Springer Book Archive

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