Abstract
The relation between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. We show that if the generalized function generated by a closed set has a one-sided directional derivative equal to 1 or -1, then the existence of generalized nearest points follows. We also give a partial answer to an open problem proposed by S. Fitzpatrick.
Citation
Renxing Ni. "EXISTENCE OF GENERALIZED NEAREST POINTS." Taiwanese J. Math. 7 (1) 115 - 128, 2003. https://doi.org/10.11650/twjm/1500407521
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