Abstract
In the context of metric modular spaces, introduced recently by the author, we define the notion of modular Lipschitzian maps between modular spaces, as an extension of the notion of Lipschitzian maps between metric spaces, and address a modular version of Banach’s Fixed Point Theorem for modular contractive maps. We show that the assumptions in our fixed point theorem are sharp and that it guarantees the existence of fixed points in cases when Banach’s Theorem is inapplicable.
Dedicated to Professor Panos Pardalos on the occasion of his 60th Birthday
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Acknowledgements
The author is partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057. I express my sincere gratitude to the organizers of the Conference “Optimization, Control and Applications in the Information Age” (Chalkidiki, Greece, June 15–20, 2014), Sergiy Butenko and Athanasios Migdalas, for an exceptionally nice work-and-leisure atmosphere of the event and the linear (nonparallel) order of presentations, which gave a pleasant feeling of completeness in that every talk could have been attended and appreciated.
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Chistyakov, V.V. (2015). Modular Lipschitzian and Contractive Maps. In: Migdalas, A., Karakitsiou, A. (eds) Optimization, Control, and Applications in the Information Age. Springer Proceedings in Mathematics & Statistics, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-18567-5_1
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DOI: https://doi.org/10.1007/978-3-319-18567-5_1
Publisher Name: Springer, Cham
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