Bayoumi Quasi-Differential is different from Fréchet-Differential

• Autorzy: Aboubakr Bayoumi
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Infinite-dimensional spaces; nonlocally convex F-spaces; quasi-differential (Super or Bayoumi-differential); Fréchet differential; optimization theory in finite-dimensional spaces; 32k1; 46A16

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 4
• Strony: 585-593

Daty

wydano

2006-12-01

online

2006-12-01

Twórcy

autor

Aboubakr Bayoumi

Bibliografia

• [1] A. Bayoumi: Foundations of Complex Analysis in Non Locally Convex Spaces, Functions theory without convexity condition, North Holland, Mathematical studies, Vol. 193, 2003.
• [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.
• [4] A. Bayoumi: “Fundamental Theorem of Calculus for locally bounded spaces”, Journal of Natural Geometry, London, Vol. 15(1–2), (1999), pp. 101–106.
• [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
• [7] B.S. Chae: Holomorphy and calculus in normed spaces, Marcel Dekker, 1985.
• [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.

Identyfikatory

DOI

10.2478/s11533-006-0028-3