Some results related to Bessel's inequality in inner product spaces
نویسندگان
چکیده
منابع مشابه
A Counterpart of Bessel’s Inequality in Inner Product Spaces and Some Grüss Type Related Results
A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Grüss type inequalities are also provided.
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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.
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Some companions of Grüss inequality in inner product spaces and applications for integrals are given.
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∥ ≤ 1 2 |Γ− γ| holds, then we have the inequality (1.3) |〈x, y〉 − 〈x, e〉 〈e, y〉| ≤ 1 4 |Φ− φ| |Γ− γ| . The constant 1 4 is best possible in the sense that it cannot be replaced by a smaller constant. The following particular instances for integrals and means are useful in applications. Corollary 1. Let f, g : [a, b] → K (K = C,R) be Lebesgue measurable and such that there exists the constants φ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2019
ISSN: 1846-579X
DOI: 10.7153/jmi-2019-13-15