Abstract
Fixed point theorems have been used in many instances in approximation theory. To prove existence of best approximants see, for example, Brandt [21], Brosowski [23], Ky Fan [86], Hicks and Humphries [114], Reich [230], Sahney, Singh, and Whitfield [244], Singh [271] [270] [269], Singh and Watson [275], and Subrahmanyam [278]. For different types of applications of fixed point theorems (mainly Schauder’s fixed point theorem) see Brosowski [23], Klee [151], Meinardus [188], and Vlasov [302]. Application of the fixed-point theorem to simultaneous best approximation is given by Sahney and Singh [243]. For further references and a survey of the subject, we refer to Brosowski [24] and Cheney [47].
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© 1997 Springer Science+Business Media Dordrecht
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Singh, S., Watson, B., Srivastava, P. (1997). Application of Fixed Points to Approximation Theory. In: Fixed Point Theory and Best Approximation: The KKM-map Principle. Mathematics and Its Applications, vol 424. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8822-5_5
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DOI: https://doi.org/10.1007/978-94-015-8822-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4918-6
Online ISBN: 978-94-015-8822-5
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