Operator refinements of Schwarz inequality in inner product spaces

2018 ◽  
Vol 67 (9) ◽  
pp. 1839-1855
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

scholarly journals On Reverses of Some Inequalities inn-Inner Product Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-22
Author(s):  
Renu Chugh ◽  
Sushma Lather
Keyword(s):  
Schwarz Inequality ◽  
Integral Inequalities ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

We present some new reverses of Cauchy-Bunyakovsky-Schwarz inequality, and Triangle and Boas-Bellman Type inequalities inn-inner product spaces. The results obtained generalize the results of Dragomir (2003–2005) inn-inner product spaces. Also we provide some applications for determinantal integral inequalities.

scholarly journals An extension of the schwarz inequality in inner product spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5329-5335
Author(s):  
Yun Ye
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Complex Numbers ◽  
Product Spaces ◽  
Inner Product Spaces

We extend the improved Schwarz inequality of Dragomir [1, Theorem 2] to any power p ? 2, ||x||p||y||p-|?x,y?|p ? |det [|?x,e?| |?y,e?|(||y||p - |?x,e?|p)1/p (||y||p- |?y,e?|p)1/p]|p for any vectors x, y, e ? Cn with ||e|| = 1. Applications to n-tuples of complex numbers are also included.

scholarly journals A generalization of Kurepa’s inequality

Filomat ◽  
2005 ◽  
pp. 7-17 ◽  
Author(s):  
Sever Dragomir
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Complex Numbers ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
De Bruijn

A generalization of Kurepa?s inequality in inner product spaces that extends in its turn the de Bruijn refinement of the Cauchy-Buniakovsky-Schwarz inequality for sequences of real and complex numbers is given.

scholarly journals More on reverse triangle inequality in inner product spaces

2005 ◽  
Vol 2005 (18) ◽  
pp. 2883-2893 ◽  
Author(s):  
A. H. Ansari ◽  
M. S. Moslehian
Keyword(s):  
Product Space ◽  
Triangle Inequality ◽  
Schwarz Inequality ◽  
Unit Vector ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Generalized Triangle Inequality

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.

scholarly journals KETAKSAMAAN CAUCHY SCHWARZ PADA RUANG HASIL KALI DALAM-2

2009 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Sri Maryani
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Gram Matrix ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Gram Determinant

Cauchy-Schwarz inequality is an important property on inner product spaces. This inequality can be generalized to 2-inner product spaces. We can be inducted a norm from those inner product spaces and then generalized that norm to 2-norm. This paper will reprove Cauchy-Schwarz inequality used positive semi definite of Gram matrix such that sub-matrix of Gram determinant is non-negative.

scholarly journals On the Cauchy- Schwarz Inequality for Vectors in the inner Product spaces with Applications

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Khalid Abd Elrazig Awad Alla Elnour
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Multiple Relationships ◽  
Product Spaces ◽  
Inner Product Spaces

In this paper, eleven different proofs for Cauchy Schwarz inequality are considered on the inner product spaces, and specific teqnique of the inequality was used to establish various proofs of some new related inequalities are obtained, Which contributed to the establishment of different mathematical inequalities, notably the application, which shows multiple relationships on the sides of the triangle.

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