Geodesic
Derivative of the norm of a linear mapping and its application to differential equations
Applications of Mathematics, Tome 37 (1992) no. 3, pp. 193-199

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MR Zbl
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
DOI : 10.21136/AM.1992.104503
Classification : 34A30, 34G10, 47A30, 47N20
Keywords: derivative of the norm of a linear mapping; linear differential equations in a Banach space; normed space; solution of the differential equation 
Tumajer, František. Derivative of the norm of a linear mapping and its application to differential equations. Applications of Mathematics, Tome 37 (1992) no. 3, pp. 193-199. doi: 10.21136/AM.1992.104503
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[1] A. N. Kolmogorov S. V. Fomin: Foundations of the theory of functions and functional analysis. (Russian). Czech translation, Praha, 1975.

[2] J. Dieudonné: Foundations of modern analysis. Academic Press, New York-London, 1960; Russian translation, Mir, Moscow. | MR

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