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Some results on best approximation in spaces with convex structure

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Analysis in Theory and Applications

Abstract

Some generalizations of the result proved by S. P. Singh [J. Approx. Theory 25(1979), 89–90] are presented in convex metric spaces. The results proved contain several known results on the subject.

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References

  1. Beg, I., Shahzad, N. and Iqbal, M., Fixed Point Theorems and Best Approximation in Convex Metric Spaces, Approx. Theory and its Appl., 8(1992), 97–105.

    MATH  MathSciNet  Google Scholar 

  2. Brosowski, B., Fixpunktsatz in der Approximationstheorie, Mathematica (Cluj), 11(1969), 195–220.

    MathSciNet  Google Scholar 

  3. Dotson, W. G., Fixed Point Theorems for Nonexpansive Mappings on Starshaped Subsets of Banach Spaces, J. London Math. Soc., 4(1972), 408–410.

    Article  MATH  MathSciNet  Google Scholar 

  4. Guay, M. D., Singh, K. L. and Whitfield, J. M. H., Fixed Point Theorems for Nonexpansive Mappings in Convex Metric Spaces, Proc. Conference on Nonlinear Analysis (Ed. S.P. Singh and J.H. Bury) Marcel Dekker, 80(1982), 179–189.

  5. Hicks, T. L. and Humphires, M. D., A Note on Fixed Point Theorems, J. Approx. Theory, 34(1982), 221–225.

    Article  MATH  MathSciNet  Google Scholar 

  6. Jungck, G., An iff Fixed Point Criterion, Math. Mag., 49(1976), 32–34.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jungck, G., Common Fixed Points for Commuting and Compatible Maps on Compacta, Proc. Amer. Math. Soc., 103(1988), 977–983.

    Article  MATH  MathSciNet  Google Scholar 

  8. Jungck, G. and Sessa, S., Fixed Point Theorems in Best Approximation Ttheory, Math. Japonica, 42(1995), 249–252.

    MATH  MathSciNet  Google Scholar 

  9. Park, S., Fixed Points of f-contractive Maps, Rocky mountain J. Math., 8(1978), 743–750.

    Article  MATH  MathSciNet  Google Scholar 

  10. Salem, A., Sahab and Khan, M. S., Some Results on Bbest Approximation, Review of Research, 17(1987), 143–151.

    Google Scholar 

  11. Salem A., Sahab and Khan, M. S., Best Approximation in Spaces with Convex Structure, Bull. Inst. Maths. Academia Sinica, 17(1989), 75–79.

    MATH  Google Scholar 

  12. Salem A., Sahab and Khan, M. S., A Result in Best Approximation Theory, J. Approx. Theory, 55(1988), 349–351.

    Article  MathSciNet  Google Scholar 

  13. Singh, S. P., An Application of a Fixed-point Theorem to Approximation Theory, J. Approx. Theory, 25(1979), 89–90.

    Article  MATH  MathSciNet  Google Scholar 

  14. Singh, S. P., Application of Fixed Point Theorems in Approximation Ttheory, Applied Nonlinear Analysis (Ed. V. Lakshmikantham) Academic Press, New York, (1979), 389–394.

    Google Scholar 

  15. Takahashi, W., A Convexity in Metric Spaces and Nonexpansive Mappings I, Kodai Math. Sem. Rep., 22(1970), 142–149.

    Article  MATH  MathSciNet  Google Scholar 

  16. Al-Thagafi, M. A., Best Approximation and Fixed Points in Strong M-starshaped Metric Spaces, Internat. J. Math. and Math. Sci., 18(1995), 613–616.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, India

    T. D. Narang

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  1. T. D. Narang
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Correspondence to T. D. Narang.

Additional information

This research is partially supported by University Grants Commission, India (F30-238/2004(SR)).

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Narang, T.D. Some results on best approximation in spaces with convex structure. Anal. Theory Appl. 24, 67–73 (2008). https://doi.org/10.1007/s10496-008-0067-7

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  • DOI: https://doi.org/10.1007/s10496-008-0067-7

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