Cauchy–Schwarz inequality
Generalizations of Cauchy Schwarz inequality in unitary spaces
... The Cauchy-Schwarz inequality is one of the most important inequalities in mathemat- ...the Cauchy-Schwarz inequality ...
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More results on a functional generalization of the Cauchy Schwarz inequality
... the Cauchy-Schwarz inequality, such as an extension of the pre-Grüss inequality and a refinement of the Cauchy-Schwarz inequality via the generalized Wagner ...
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A Generalization of the Cauchy-Schwarz Inequality with Four Free Parameters and Applications
... the Cauchy-Schwarz ...for inequality (1.1). For this purpose, first the following inequality should be considered, which is directly provable via some algebraic ...
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A Generalization of the Cauchy Schwarz Inequality with Eight Free Parameters
... The results of the recent published paper by Masjed-Jamei et al. 2009 are extended to a larger class and some of subclasses are studied in the sequel. In other words, we generalize the well known ...
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Inequalities Of Schwarz Type For n-Tuples Of Vectors In Inner Product Spaces With Applications
... corresponding Cauchy-Schwarz ...of Cauchy-Schwarz inequality in unitary spaces, ...of Cauchy-Schwarz inequality in ...
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Generalized Norms Inequalities for Absolute Value Operators
... In this section, we generalize some unitarily invariant norms inequalities for ab- solute value operators. Our results based on several lemmas. First two lemmas contain norm inequalities of Minkowski type and generalized ...
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Converses of the Cauchy-Schwartz Inequality in the C*-framework
... the inequality in (2.2). Based on the variance inequality in noncommutative probability theory, ...the Cauchy-Schwarz inequality in a noncommutative ...
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RRRR Specifically the dot product of two vectors a
... the Cauchy – Schwarz inequality allows one to define a notion of “the angle between the two vectors” for an arbitrary inner product, where the extendibility of such concepts from Euclidean geometry ...
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Spectral Radii of Operators and High-Power Operator Inequalities
... the inequality |(T x, y)| 2 ≤ (T x, x)(T y, y) holds for T ≥ 0 and for all x, y ∈ H (consider the unique positive square root of T ...the Cauchy-Schwarz inequality, and this is crucial in the ...
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Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables
... the Cauchy-Schwarz inequality (3) is the mathematical foundation of the Heisenberg uncertainty relation ...generalized Cauchy-Schwarz inequality for multiple vectors, and ...
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Additive functional inequalities in 2 Banach spaces
... The further part of the proof is similar to the proof of Theorem .. Now we prove the superstability of the Cauchy functional inequality in -Banach spaces. Theorem . Let θ ∈ [, ∞), p, q, r, t ∈ (, ∞) ...
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Approximate Cauchy functional inequality in quasi Banach spaces
... The method which was provided by Hyers, and which produces the additive mapping h, was called a direct method. This method is the most important and most powerful tool for studying the stability of various functional ...
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Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
... For other trace inequalities see [7], [18], [41], [33], [51], [58], [74] and [80]. In this paper we survey some recent trace inequalities obtained by the author for operators in Hilbert spaces that are connected to ...
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Lecture2
... An important property of vectors connecting the notions of inner product and norm is the Cauchy-Schwartz inequality. Theorem 2.2 (Cauchy-Schwartz)[r] ...
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A Refinement of Jensen's Discrete Inequality for Differentiable Convex Functions
... Analytic Inequality Theory is determined by the fact that many other fundamental results such as: the Arithmetic Mean – Geometric Mean – Harmonic Mean inequality, or the H¨ older and Minkowski inequalities, ...
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On the Cauchy Functional Inequality in Banach Modules
... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. ...
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A Cauchy type inequality for Möbius operations
... a Cauchy type inequality and a criterion for convergence of series for the restriction of Möbius operations to the open ...classical Cauchy inequality and convergence of se- ries have ...
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Norm Inequalities for Sequences of Operators Related to the Schwarz Inequality
... Some norm inequalities for sequences of linear operators defined on Hilbert spaces that are related to the classical Schwarz inequality are given.. Applications for vector inequalities a[r] ...
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Reverses of the Schwarz Inequality in Inner Product Spaces and Applications
... Recent reverses for the celebrated Schwarz inequality in inner product spaces and applications for discrete and integral inequalities are sur- veyed1. Introduction.[r] ...
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Dual Orlicz Harmonic Mixed Quermassintegrals
... the Grassmannian manifold of i-dimensional linear sub- spaces of R n , the normalized Haar measure on G(n, i) and the i-dimensional volume of slice of K by an i − dimensional subspace ξ ⊂ R n , respectively. Equation (5) ...
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