# Bayoumi Quasi-Differential is different from Fréchet-Differential

Open Mathematics (2006)

- Volume: 4, Issue: 4, page 585-593
- ISSN: 2391-5455

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topAboubakr Bayoumi. "Bayoumi Quasi-Differential is different from Fréchet-Differential." Open Mathematics 4.4 (2006): 585-593. <http://eudml.org/doc/269783>.

@article{AboubakrBayoumi2006,

abstract = {We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex},

author = {Aboubakr Bayoumi},

journal = {Open Mathematics},

keywords = {32k1; 46A16},

language = {eng},

number = {4},

pages = {585-593},

title = {Bayoumi Quasi-Differential is different from Fréchet-Differential},

url = {http://eudml.org/doc/269783},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Aboubakr Bayoumi

TI - Bayoumi Quasi-Differential is different from Fréchet-Differential

JO - Open Mathematics

PY - 2006

VL - 4

IS - 4

SP - 585

EP - 593

AB - We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex

LA - eng

KW - 32k1; 46A16

UR - http://eudml.org/doc/269783

ER -

## References

top- [1] A. Bayoumi: Foundations of Complex Analysis in Non Locally Convex Spaces, Functions theory without convexity condition, North Holland, Mathematical studies, Vol. 193, 2003. Zbl1082.46001
- [2] A. Bayoumi: “Mean-Value Theorem for complex locally bounded spaces”, Communication in Applied Non-Linear Analysis, Vol. 4(3), (1997).
- [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 Integral of vector-valued functions of p-Banach spaces”, Algebra, Groups and Geometries, Vol. 22(4), (2005).
- [6] A. Bayoumi: “Bolzano’s Intermediate-Value Theorem for Quasi-Holomorphic Maps”, Central European Journal of Mathematics, Vol. 3(1), (2005), pp. 76–82. http://dx.doi.org/10.2478/BF02475656 Zbl1069.46508
- [7] B.S. Chae: Holomorphy and calculus in normed spaces, Marcel Dekker, 1985. Zbl0571.46031
- [8] I.J. Corwin and R.H. Szczarba: Multivariable Calculus, Marcel Dekker, 1982.
- [9] S. Rolewicz: Metric linear spaces, Monografje Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk, 1972. Zbl0226.46001

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