Reverses of the Triangle Inequality in Inner Product Spaces
نویسنده
چکیده
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
منابع مشابه
Quadratic Reverses of the Triangle Inequality in Inner Product Spaces
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
متن کاملm at h . FA ] 1 F eb 2 00 5 Refinements of Reverse Triangle Inequalities in Inner Product Spaces ∗
Refining some results of S. S. Dragomir, several new reverses of the triangle inequality in inner product spaces are obtained.
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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 if a is 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}, and αr,s = min{(r2‖x...
متن کاملar X iv : m at h / 05 06 19 8 v 1 [ m at h . FA ] 1 0 Ju n 20 05 More on Reverse Triangle Inequality in Inner Product Spaces ∗
Refining some results of S. S. 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 if a is 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} and αr,s ...
متن کاملSome Reverses of the Generalised Triangle Inequality in Complex Inner Product Spaces
was first discovered by M. Petrovich in 1917, [5] (see [4, p. 492]) and subsequently was rediscovered by other authors, including J. Karamata [2, p. 300 – 301], H.S. Wilf [6], and in an equivalent form by M. Marden [3]. The first to consider the problem of obtaining reverses for the triangle inequality in the more general case of Hilbert and Banach spaces were J.B. Diaz and F.T. Metcalf [1] who...
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