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Vol.17 No.2
Abstract
Let <TEX>$\cal{A}$</TEX> be a unital Banach algebra. If f : <TEX>$\cal{A}{\rightarrow}\cal{A}$</TEX> is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : <TEX>$\cal{A}{\rightarrow}\cal{A}$</TEX> is anexactly quadratic derivation. On the other hands, let <TEX>$\cal{A}$</TEX> and <TEX>$\cal{B}$</TEX> be Banach algebras.Any approximately generalized homomorphism f : <TEX>$\cal{A}{\rightarrow}\cal{B}$</TEX> corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.
Abstract
Throught this paper, we will investigate some properties of left regular and strongly reduced near-rings. Mason introduced the notion of left regularity and he characterized left regular zero-symmetric unital near-rings. Also, this concept have been studied by several authors. The purpose of this paper is to find some characterizations of the strong reducibility in near-rings, and the strong regularity in near-rings which are closely related with strongly reduced near-rings.
Abstract
Category Fuz of fuzzy sets has a similar function to the Category Set. But it forms a weak topos. We study a natural number object and a weak natural number object in the weak topos Fuz. Also we study the weak natural number object in <TEX>$Fuz^C$</TEX>.
Abstract
In this paper, we introduce the concepts of faintly <TEX>${\gamma}$</TEX>-continuity and extremely <TEX>${\gamma}$</TEX>-closed graph. And we study characterizations of such functions and relationships between faintly <TEX>${\gamma}$</TEX>-continuity and extremely <TEX>${\gamma}$</TEX>-closed graph.
Abstract
The object of the present paper is to introduce <TEX>${\Lambda}$</TEX>-dual and the concept of sectional analyticity (Abschinitts-anatytique or AA property) of an FK-space.The motivation for AA-property is that a sequence space having AK-property possess AA-property.
Abstract
Let (M,p) be a germ of a <TEX>$C^{\infty}$</TEX> CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a <TEX>$C^{\infty}$</TEX> contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in <TEX>$\mathbb{C}^{n+d}$</TEX> defined by a vector valued weighted homogeneous polynomial.
Abstract
In this paper, we introduce the concept of a weakly P-space which is a generalization of a P-space and prove that for any covering map f : <TEX>$X{\rightarrow}Y$</TEX>, X is a weakly P-space if and only if Y is a weakly P-space. Using these, we investigate the minimal basically disconnected cover of weakly P-spaces and their products.
Abstract
Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.
Abstract
In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.
Abstract
We give an upper bound for the estimation of the difference between both sides of the well-known H<TEX>$\ddot{o}$</TEX>lder's inequality. Moreover, an upper bound for the estimation of the difference of the integral form of H<TEX>$\ddot{o}$</TEX>lder's inequality is also obtained. The results of this paper are natural generalizations and refinements of those of [2-4].