Some inequalities in inner product spaces related to the generalized triangle inequality
نویسندگان
چکیده
منابع مشابه
Some inequalities in inner product spaces related to the generalized triangle inequality
In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear spaces are also obtained.
متن کاملA note on "Some inequalities in inner product spaces related to the generalized triangle inequality" by S.S. Dragomir et al
In a recent paper [1], Dragomir et al. proposed the open problem of whether constant 2, appearing in the following two theorems, is the best possible. In this short note, we answer in affirmative sense this question. Theorem 1 [1, Theorem 6]. Let (H;h , i) be an inner product space, xi 2 H, for all i 2 {1, . . .,n} and pi P 0 with Pn i1⁄41pi 1⁄4 1. Suppose there exist constants ri > 0, i 2 {1, ...
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Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
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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.
متن کاملMore on reverse triangle inequality in inner product spaces
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...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2011
ISSN: 0096-3003
DOI: 10.1016/j.amc.2011.02.046