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

Open Mathematics (2005)

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

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topAboubakr 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

top- [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] A. Bayoumi: “Mean-Value Theorem for complex locally bounded spaces”, Communication in Applied Nonlinear Analysis, Vol. 4(3), (1997). Zbl0910.46032
- [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] 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] A. Bayoumi: “Mean-Value Theorem for definite integrals of vector-valued maps of p-Banach spaces”, (2005), to appear. Zbl1110.26021
- [6] M. Kransnoseliski: Topological method in theory of nonlinear integral equations, Mcmillan, 1964.
- [7] S. Rolewicz: Metric linear spaces, Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk, 1972. Zbl0226.46001
- [8] J.T. Schwartz: Nonlinear functional analysis, Gordon and Breach, New York, 1969.
- [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] 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] D. Smart: Fixed points theorems, Cambridge Tracts in Math., Vol. 66, 1974.
- [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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