Diethard Pallaschke, Dieter Pumplün (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
F. A. Toranzos (1971)
Colloquium Mathematicae
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Clyde F. Martin, J. E. Valentine (1976)
Colloquium Mathematicae
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P. P. Zabrejko (1997)
Collectanea Mathematica
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We give a short survey on some fixed point theorems which are generalizations of the classical Banach-Caccioppoli principle of contractive mappings. All these results are gathered in three theorems about existence and uniqueness of fixed points for operators which act in K-metric or K-normed linear spaces and, in particular, in local convex spaces and scales of Banach spaces. Three fixed point theorems presented in this article cover numerous applications in numerical methods, theory...
Janusz Matkowski (1987)
Acta Universitatis Carolinae. Mathematica et Physica
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E.R. Lorch (1952)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Janusz Matkowski, Małgorzata Wróbel (2012)
Open Mathematics
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We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.
Farag, Mark, Van Der Merwe, Brink (2010)
International Journal of Mathematics and Mathematical Sciences
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S. Czerwik (1976)
Matematički Vesnik
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Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama (2014)
Formalized Mathematics
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In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences...
Jebril, Iqbal Hamzh, Noorani, Mohd.Salmi Md., Saari, Ahamad Shabir (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Noboru Endou, Yasunari Shidama, Katsumasa Okamura (2006)
Formalized Mathematics
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As application of complete metric space, we proved a Baire's category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space.