A result on best approximation in p -normed spaces

Abdul Latif

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 1, page 71-75
  • ISSN: 0044-8753

Abstract

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We study best approximation in p -normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.

How to cite

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Latif, Abdul. "A result on best approximation in $p$-normed spaces." Archivum Mathematicum 037.1 (2001): 71-75. <http://eudml.org/doc/248749>.

@article{Latif2001,
abstract = {We study best approximation in $p$-normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.},
author = {Latif, Abdul},
journal = {Archivum Mathematicum},
keywords = {best approximation; common fixed point; f-nonexpansive map; common fixed points; -normed spaces; best approximation},
language = {eng},
number = {1},
pages = {71-75},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A result on best approximation in $p$-normed spaces},
url = {http://eudml.org/doc/248749},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Latif, Abdul
TI - A result on best approximation in $p$-normed spaces
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 1
SP - 71
EP - 75
AB - We study best approximation in $p$-normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.
LA - eng
KW - best approximation; common fixed point; f-nonexpansive map; common fixed points; -normed spaces; best approximation
UR - http://eudml.org/doc/248749
ER -

References

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  1. Brosowski B., Fixpunktsatze in der approximations theorie, Mathematica (Cluj) 11 (1969), 195–220. (1969) MR0277979
  2. Carbone A., Applications of fixed point theorems, Jnanabha 19 (1989), 149–155. (1989) Zbl0718.41042MR1060662
  3. Dotson W. G., Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1972), 408–410. (1972) MR0296778
  4. Hicks T. L., Humphries M. D., A note on fixed point theorems, J. Approx. Theory 34 (1982), 221–225. (1982) Zbl0483.47039MR0654288
  5. Jungck G., Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261–263. (1976) Zbl0321.54025MR0400196
  6. Jungck G., Sessa S., Fixed point theorems in best approximation theory, Math. Japon. 42 (1995), 249–252. (1995) Zbl0834.54026MR1356383
  7. Kirk W. A., Fixed point theory for nonexpansive mappings, Lecture Notes in Math. 886 (1981), 484–505. (1981) Zbl0479.47049MR0643024
  8. Khan L. A., Latif A., On best approximation in p -normed spaces, submitted. 
  9. Köthe G., Topological vector Spaces I, Springer-Verlag, Berlin, 1969. (1969) Zbl0179.17001MR0248498
  10. Lami Dozo E., Centres asymptotiques dans certains F-espaces, Boll. Un. Mat. Ital. B(5) 17 (1980), 740–747. (1980) Zbl0456.47049MR0580553
  11. Meinardus G., Invarianze bei Linearen Approximationen, Arch. Rational Mech. Anal. 14 (1963), 301–303. (1963) MR0156143
  12. Opial Z., Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 531–537. (1967) MR0211301
  13. Rudin W., Functional Analysis, (second edition), McGraw-Hill, New York, 1991. (1991) Zbl0867.46001MR1157815
  14. Singh S. P., An application of a fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89–90. (1979) Zbl0399.41032MR0526280

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