Abstract
In the paper we present the generalized Minkowski functionals. We also establish some useful properties of the Minkowski functionals, criterium of the continuity of such functionals, and a generalization of a Kolmogorov result.
In Honor of Constantin Carathéodory
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References
Czerwik, S.: Functional Equations and Inequalities in Several Variables, 410 pp. World Scientific, Singapore (2002)
Diaz, J.B., Margolis, B.: A fixed point theorem of the alternative, for contractions on a generalized complete metric space. Bull. Am. Math. Soc. 74, 305–309 (1968)
Dugundji, J., Granas, A.: Fixed Point Theory, pp. 5–209. Polish Scientific Publishers, Warsaw (1982)
Kolmogorov, A.N.: Zur Normierbarkeit eines allgemeinen topologischen linearen Raümes. Stud. Math. 5, 29–34 (1934)
Luxemburg, W.A.J.: On the convergence of successive approximations in the theory of ordinary differential equations, III. Nieuw. Arch. Wisk. (3) 6, 93–98 (1958)
Rolewicz, S.: Functional Analysis and Control Theory (in Polish), 393 pp. Polish Scientific Publishers, Warsaw (1977)
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Czerwik, S., Król, K. (2016). Generalized Minkowski Functionals. In: Pardalos, P., Rassias, T. (eds) Contributions in Mathematics and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-31317-7_4
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DOI: https://doi.org/10.1007/978-3-319-31317-7_4
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Online ISBN: 978-3-319-31317-7
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