2-Inner Product Spaces
Some Inequalities in 2-inner Product Spaces
... in 2 − inner product spaces in con- nection to A´ czel’s inequality ...in inner products, see [8]. We note that the results obtained here, in 2 − inner product ...
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Atomic Systems in 2-inner Product Spaces
... a 2-inner product space is introduced and then this concept is generalized to an atomic system for an ...in 2-inner product ...
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On Bessel's and Grüss' Inequalities for Orthornormal Families in 2-Inner Product Spaces and Applications
... of 2-inner products and 2-inner product spaces have been inten- sively studied by many authors in the last three ...of 2-inner product spaces as well ...
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On Some Grüss Type Inequality in 2-Inner Product Spaces and Applications
... In this paper, we shall give a generalization of the Gr¨ uss type inequality and obtain some applications of the Gr¨ uss type inequality in terms of 2-inner product spaces.. 1..[r] ...
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Some Grüss' Type Inequalities in 2-Inner Product Spaces and Applications for Determinantal Integral Inequalities
... complex 2-inner product ...of 2-inner product spaces, some determinantal integral inequalities for synchronous functions are pointed out as ...
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On 2-Inner Product Spaces and Reproducing Kernel Property
... section 2, we prepare some preliminaries of 2-inner product spaces and review some important and useful theorems and ...defined 2-inner product reproducing kernel ...
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Generalized Dunkl Williams inequality in 2 inner product spaces
... and (.) and obtained a generalization of inequalities (.) and (.). This paper contains two sections. In the first section, we will work on a generalized case of Dunkl-Williams inequality in -normed spaces ...
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On Reverses of Some Inequalities in n Inner Product Spaces
... of 2-norm and 2-inner product spaces as generalization of norm and inner product ...of 2-inner product spaces can be found in the book in ...
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6. Some New Properties of Inner Product Quasilinear Spaces
... In this paper, motivated by the work of Assev [2] and Markow [8], we introduce new concepts on inner product quasilinear spaces and prove some theorems related to these notions. Moreover, we ...
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Inequalities for Hypo-q-Norms on a Cartesian Product of Inner Product Spaces
... an inner product space over the real or complex number …eld K ...an inner product space over the real or complex number …eld K ...x 2 H n with x = (x 1 ; : : : ; x n ) ; we ...
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A Survey on Generalized Inner Product Spaces and Strong Topologies
... Where k=1,....,n . thus the operations of the vector summation is continuous that similarly we can show that the operation of multiplication, by a scalar is continuous. The rest follows from lemma 1 and 2 ...
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More on reverse triangle inequality in inner product spaces
... Using several ideas and following the terminology of [4, 5], we modify or refine some results of Dragomir and ours [1] and get some new reverses of triangle inequality. Among several results, we show that if a is a unit ...
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A Potpourri of Schwarz Related Inequalities in Inner Product Spaces
... δ+∆ 2 , δ, ∆ ∈ K , with γ = Re (∆¯ γ) > 0, then the condition |β| 2 ≥ αγ is equivalent to |δ + ∆| 2 ≥ 4 Re (∆¯ γ) which is actually |∆ − δ| 2 ≥ ...
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Reverses of the Schwarz Inequality in Inner Product Spaces and Applications
... Let r = √ ε > 0, ε ∈ (0, 1) , a, e ∈ H with kak = kek = 1 and a ⊥ e. Put x = a + √ εe. Then obviously x ∈ B (a, r) , kak > r and kxk 2 = kak 2 + ε kek 2 = 1 + ε, Re hx, ai = kak 2 = 1, ...
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Fixed Points, Inner Product Spaces, and Functional Equations
... 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 ...
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A Functional equation related to inner product spaces in non archimedean normed spaces
... The first stability problem concerning group homomorphisms was raised by Ulam [1] in 1940 and affirmatively solved by Hyers [2]. The result of Hyers was generalized by Aoki [3] for approximate additive mappings ...
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On the Bombieri Inequality in Inner Product Spaces
... kxk 2 × ...
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Inner Product Spaces for Bayesian Networks
... As a second topic, we investigate a class of probabilistic models known as logistic autoregres- sive Bayesian networks or sigmoid belief networks. These networks were originally proposed by McCullagh and Nelder (1983) ...
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A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials
... A reverse of the triangle inequality in inner product spaces re- lated to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given1. Diaz and F.T.[r] ...
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A Potpourri of Schwarz Related Inequalities in Inner Product Spaces (II)
... DRAGOMIR, Inequalities for orthornormal families of vectors in inner product spaces related to Buzano’s, Richard’s and Kurepa’s results, RGMIA Res.. Pure & Appl.[r] ...
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