Bolzano’s intermediate-value theorem for quasi-holomorphic maps

Aboubakr Bayoumi

Open Mathematics (2005)

  • Volume: 3, Issue: 1, page 76-82
  • ISSN: 2391-5455

Abstract

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We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.

How to cite

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Aboubakr Bayoumi. "Bolzano’s intermediate-value theorem for quasi-holomorphic maps." Open Mathematics 3.1 (2005): 76-82. <http://eudml.org/doc/268911>.

@article{AboubakrBayoumi2005,
abstract = {We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.},
author = {Aboubakr Bayoumi},
journal = {Open Mathematics},
keywords = {46A16; 46E50},
language = {eng},
number = {1},
pages = {76-82},
title = {Bolzano’s intermediate-value theorem for quasi-holomorphic maps},
url = {http://eudml.org/doc/268911},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Aboubakr Bayoumi
TI - Bolzano’s intermediate-value theorem for quasi-holomorphic maps
JO - Open Mathematics
PY - 2005
VL - 3
IS - 1
SP - 76
EP - 82
AB - We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.
LA - eng
KW - 46A16; 46E50
UR - http://eudml.org/doc/268911
ER -

References

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  1. [1] A. Bayoumi: Foundations of complex analysis in non locally convex spaces. Functions theory without convexity conditions, Mathematics studies, Vol. 193, North Holland, 2003. Zbl1082.46001
  2. [2] A. Bayoumi: “Mean-Value Theorem for complex locally bounded spaces”, Communication in Applied Nonlinear Analysis, Vol. 4(3), (1997). Zbl0910.46032
  3. [3] A. Bayoumi: “Mean-Value Theorem for real locally bounded spaces”, Journal of Natural Geometry, London, Vol. 10, (1996), pp. 157–162. Zbl0858.46035
  4. [4] A. Bayoumi: “Fundamental theorem of calculus for locally bounded spaces”, Journal of Natural Geometry, London, Vol. 15(1–2), (1999), pp. 101–106. Zbl0933.46037
  5. [5] A. Bayoumi: “Mean-Value Theorem for definite integrals of vector-valued maps of p-Banach spaces”, (2005), to appear. Zbl1110.26021
  6. [6] M. Kransnoseliski: Topological method in theory of nonlinear integral equations, Mcmillan, 1964. 
  7. [7] S. Rolewicz: Metric linear spaces, Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk, 1972. Zbl0226.46001
  8. [8] J.T. Schwartz: Nonlinear functional analysis, Gordon and Breach, New York, 1969. 
  9. [9] M.H. Shih: “An analogy of Bolzano’s theorem for functions of a complex variable”, Amer. Math. Monthly, Vol. 89, (1982), pp. 210–211. http://dx.doi.org/10.2307/2320206 Zbl0494.30010
  10. [10] M.H. Shih: “Bolzano’s theorem in several complex variables”, Proc. Amer. Math. Soc., Vol. 79, (1980), pp. 32–34. http://dx.doi.org/10.2307/2042381 Zbl0455.32002
  11. [11] D. Smart: Fixed points theorems, Cambridge Tracts in Math., Vol. 66, 1974. 
  12. [12] K. Wlodraczyk: “Intermediate value theorem for holomorphic maps in complex Banach spaces”, Math. Proc. Camb. Phil. Sco., (1991), pp. 539–540. Zbl0744.46036

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