ISSN : 1226-0657
Let N be a right near-ring. N is said to be strongly reduced if, for <TEX>$a\inN$</TEX>, <TEX>$a^2 \in N_{c}$</TEX> implies <TEX>$a\;\in\;N_{c}$</TEX>, or equivalently, for <TEX>$a\inN$</TEX> and any positive integer n, <TEX>$a^{n} \in N_{c}$</TEX> implies <TEX>$a\;\in\;N_{c}$</TEX>, where <TEX>$N_{c}$</TEX> denotes the constant part of N. We will show that strong reducedness is equivalent to condition (ⅱ) of Reddy and Murty's property <TEX>$(^{\ast})$</TEX> (cf. [Reddy & Murty: On strongly regular near-rings. Proc. Edinburgh Math. Soc. (2) 27 (1984), no. 1, 61-64]), and that condition (ⅰ) of Reddy and Murty's property <TEX>$(^{\ast})$</TEX> follows from strong reducedness. Also, we will investigate some characterizations of strongly reduced near-rings and their properties. Using strong reducedness, we characterize left strongly regular near-rings and (<TEX>$P_{0}$</TEX>)-near-rings.
Let R be a prime ring with characteristic different from two and let <TEX>$\theta,\varphi,\sigma,\tau$</TEX> be the automorphisms of R. Let d : <TEX>$R{\rightarrow}R$</TEX> be a nonzero (<TEX>$\theta,\varphi$</TEX>)-derivation. We prove the following results: (i) if <TEX>$a{\in}R$</TEX> and [d(R), a]<TEX>$_{{\theta}o{\sigma},{\varphi}o{\tau}}$</TEX>=0, then <TEX>$\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, the center of R, (ii) if <TEX>$d([R,a]_{\sigma,\;\tau)\;=\;0,\;then\;\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, (iii) if <TEX>$[ad(x),\;x]_{\sigma,\;\tau}\;=\;0;for\;all\;x\;\in\;RE$</TEX>, then a = 0 or R is commutative.
Let <TEX>$\cal{K}$</TEX> be the extension Hilbert space of a Hilbert space <TEX>$\cal{H}$</TEX> and let <TEX>$\Phi$</TEX> be the faithful <TEX>$\ast$</TEX>-representation of <TEX>$\cal{B}(\cal{H})$</TEX> on <TEX>$\cal{k}$</TEX>. In this paper, we show that if T is an irreducible <TEX>${\omega}-hyponormal$</TEX> operators such that <TEX>$ker(T)\;{\subset}\;ker(T^{*})$</TEX> and <TEX>$T^{*}T\;-\;TT^{\ast}$</TEX> is compact, then <TEX>$\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$</TEX>.
In this paper, we consider the existence of the solutions to the generalized vector variational-type inequalities for set-valued mappings on Hausdorff topological vector spaces using Fan's geometrical lemma.
In this paper, we introduce the concepts of t-intuitionistic fuzzy products and t-intuitionistic fuzzy subgroupoids. And we study some properties of t-products and t-subgroupoids.
In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].
We compare the computing times on the bicubic B-spline dueing to the algorithms.
Let <TEX>$CS_\alpha(\beta)$</TEX> denote the class of normalized strongly <TEX>$\alpha$</TEX>-close-to-convex functions of order <TEX>$\beta$</TEX>, defined in the open unit disk <TEX>$\cal{U}$</TEX> of <TEX>$\mathbb{C}$</TEX. by , <TEX>${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$</TEX> such that <TEX>$g\; \in\;S^{\ask}$</TEX>, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to <TEX>$CS_\alpha(\beta)$</TEX>.
The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then <TEX>$A^{\ast}= X<T^{\ast}B^{\ast}$</TEX>. In this paper, we show that if A is <TEX>$\omega$</TEX>-hyponormal and <TEX>$B^{\ast}$</TEX> is invertible <TEX>$\omega$</TEX>-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then <TEX>$A^{\ast}X = XB^{\ast}$</TEX>.
In the present paper, we treat a Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric <TEX>$L({\alpha},\;{\beta})\;\;C_1{\alpha}+C_2{\beta}+{\alpha}^2/{\beta}$</TEX> satisfying some conditions. We find a condition that a Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric be a Berwald space. Then it is shown that if a two-dimensional Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric is a Landsberg space, then it is a Berwald space.