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ISSN : 1226-0657
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Vol.15 No.4
Abstract
The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.
Abstract
We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.
Abstract
The notion of fuzzy abysms in Hilbert algebras is introduced, and several properties are investigated. Relations between fuzzy subalgebra, fuzzy deductive systems, and fuzzy abysms are considered.
Abstract
In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions <TEX>$\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$</TEX> are decreasing in (0, <TEX>${\infty}$</TEX>) and the function <TEX>$\frac{t}{e^{at}-e^{(a-1)t}}$</TEX> for a <TEX>$a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$</TEX> is logarithmically concave.
Abstract
In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||<TEX>${\leq}$</TEX>||f(x+y)+f(z+w)|| in normed modules over a <TEX>$C^*$</TEX>-algebra. This is applied to understand homomor-phisms in <TEX>$C^*$</TEX>-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||<TEX>${\leq}$</TEX>||f(x+y+z+w)||+<TEX>${\theta}||x||^p||y||^p||z||^p||w||^p$</TEX> in real Banach spaces, where <TEX>${\theta}$</TEX>, p are positive real numbers with <TEX>$4p{\neq}1$</TEX>.
Abstract
Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let <TEX>${\pounds}$</TEX> be a subspace lattice acting on a separable complex Hilbert space H and let X=<TEX>$(x_{ij})$</TEX> and Y=<TEX>$(y_{ij})$</TEX> be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator <TEX>$A=(a_{ij})$</TEX> in Alg<TEX>${\pounds}$</TEX> such that AX=Y. (2) There is a bounded sequence <TEX>$\{{\alpha}_n\}$</TEX> in <TEX>$\mathbb{C}$</TEX> such that <TEX>${\sum}_{n=1}^{\infty}|{\alpha}_n|^2</TEX><TEX><</TEX><TEX>{\infty}$</TEX> and <TEX>$$y1_i={\alpha}_1x_{1i}+{\alpha}_2x_{2i}$$</TEX> <TEX>$$y2k_i={\alpha}_{4k-1}x_2k_i$$</TEX> <TEX>$$y{2k+1}_i={\alpha}_{4k}x_{2k}_i+{\alpha}_{4k+1}x_{2k+1}_i+{\alpha}_{4k+2}x_{2k+2}_i\;for\;all\;i,\;k\;\mathbb{N}$$</TEX>.
Abstract
In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t <TEX>$${\in}$$</TEX> (0,1), x'(0)=0, x(1) = <TEX>$${\int}_0^1$$</TEX> x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.
Abstract
A clear-cut characterization of the matrix class <TEX>$({\ell}^{\infty}(X),\;c_0(Y))$</TEX> is obtained for a very general case.
Abstract
In this paper, we consider a new Minty's Lemma for strong implicit vector variational inequality systems and obtain some existence results for systems of strong implicit vector variational inequalities which generalize some results in [1].