Abstract
We discuss the problem of best simultaneous approximation in quotient spaces when the underlying spaces are metric linear spaces. We characterize simultaneous proximinality, simultaneous Chebyshevity, simultaneous pseudo-Chebyshevity and simultaneous quasi-Chebyshevity and see how these are transmitted to and from quotient spaces. The results proved in the paper generalize and extend several known results on the subject.
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Acknowledgements
The research work of the first author has been supported by U.G.C. under Emeritus Fellowship and that of the second author under U.G.C., Senior Research Fellowship.
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Narang, T.D., Gupta, S. (2016). Best Simultaneous Approximation in Quotient Spaces. In: Cushing, J., Saleem, M., Srivastava, H., Khan, M., Merajuddin, M. (eds) Applied Analysis in Biological and Physical Sciences. Springer Proceedings in Mathematics & Statistics, vol 186. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3640-5_21
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DOI: https://doi.org/10.1007/978-81-322-3640-5_21
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