More on reverse triangle inequality in inner product spaces
2005 ◽
Vol 2005
(18)
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pp. 2883-2893
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Keyword(s):
Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that ifais a unit vector in a real or complex inner product space(H;〈.,.〉),r,s>0,p∈(0,s],D={x∈H,‖rx−sa‖≤p},x1,x2∈D−{0}, andαr,s=min{(r2‖xk‖2−p2+s2)/2rs‖xk‖:1≤k≤2}, then(‖x1‖‖x2‖−Re〈x1,x2〉)/(‖x1‖+‖x2‖)2≤αr,s.
2004 ◽
Vol 69
(2)
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pp. 327-340
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Keyword(s):
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2011 ◽
Vol 217
(18)
◽
pp. 7462-7468
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2021 ◽
Vol 3
(2)
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pp. 80
Keyword(s):
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2005 ◽
Vol 78
(2)
◽
pp. 199-210
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Keyword(s):
2020 ◽
Vol 57
(4)
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pp. 541-551
Keyword(s):