[PDF] Top 20 Atomic Systems in 2-inner Product Spaces

... Frames in Hilbert spaces were introduced by Duffin and Schaffer [9] in the context of nonharmonic Fourier series in 1952. In 1986, frames were brought to life by Daubechies et al. [7]. Now frames play an important ... See full document

... In This project we have discussed the concept of orthognality in normed space, which is an extension of the concept orthognality in Hilbert spaces. This concept has been used by Giles [2] to obtain some ... See full document

... Theorem 3. Let (X, (., .|.)) be an inner product space over K ( K = R , C ) and e, z ∈ X, ke|zk = 1. If ϕ, γ, Φ, Γ are real or complex numbers and x, y are vectors in X such that the conditions (3.3) or, ... See full document

... 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] ... See full document

... 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 ... See full document

... 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 ... See full document

... 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 ... See full document

... 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 ... See full document

... 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 ≥ ... See full document

... 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, ... See full document

... 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 ... See full document

... in inner product spaces are ...complex inner product space ( H ; · , · ), r , s > 0, p ∈ (0, s ], D = { x ∈ H , rx − sa ≤ p } , x 1 ,x 2 ∈ D − { 0 } , and α r , s = min { (r ... See full document

... The theory of quasilinear analysis is one of the fundamental theories in nonlinear analysis which has various applications such as integral and differential equations, approximation theory and bifurcation theory. In ... See full document

... The lower bounds obtained in Section 4 rely on arguments based on the VC dimension of the respec- tive concept class. In particular, a quadratic lower bound for the logistic autoregressive network has been established. ... See full document

... kxk 2 ×                                                                                                        ... See full document

... 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 ... See full document

... Abstract: This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach ... See full document

... 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 ... See full document

... 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] ... See full document

... 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] ... See full document