In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

Here we see that the $p-Ces{\grave{a}}ro$ operators, the generalized $Ces{\grave{a}}ro$ operators of order one, the discrete generalized $Ces{\grave{a}}ro$ operators, and their adjoints are all posinormal operators on ${\ell}^2$, but many of these operators are not dominant, not normaloid, and not spectraloid. The question of dominance for $C_k$, the generalized $Ces{\grave{a}}ro$ operators of order one, remains unsettled when ${\frac{1}{2}}{\leq}k<1$, and that points to some general questions regarding terraced matrices. Sufficient conditions are given for a terraced matrix to be normaloid. Necessary conditions are given for terraced matrices to be dominant, spectraloid, and normaloid. A very brief new proof is given of the well-known result that $C_k$ is hyponormal when $k{\geq}1$.

This paper is concerned with algorithm for calculating one-sided best simultaneous approximation, in the case of continuous functions. we will apply any subgradient algorithm. In other words, we consider the algotithms from a mathematical, rather then computational, point of view.

This work deals with the existence of uncountably many bounded positive solutions for the third order nonlinear neutral delay differential equation $$\frac{d^3}{dt^3}[x(t)+p(t)x(t-{\tau})]+f(t,x(t-{{\tau}_1}),{\ldots},x(t-{{\tau}_k}))=0,\;t{\geq}t_0$$ where ${\tau}>0$, ${\tau}_i{\in}{\mathbb{R}^+}$ for $i{\in}\{1,2,{\ldots},k\}$, $p{\in}C([t_0,+{\infty}),{\mathbb{R}^+})$ and $f{\in}C([t_0,+{\infty}){\times}{\mathbb{R}^k},{\mathbb{R}})$.

We first introduce a space of homogeneous type X, and develop the theory of the tent spaces on the generalized upper half-space $X{\times}(0,{\infty})$. The goal of this paper is to study that every element of the tent spaces $T_{\Omega}^{p}$($X{\times}(0,{\infty})$, $0, can be decomposed into elementary particles which are called "atoms."

If P(f, r) is the set of endpoints of radii which have length greater than or equal to r > 0 under a conformal mapping f of the unit disc. Then for large r, the logarithmic capacity of P(f, r), $\frac{1}{\sqrt[2]{r}}{\leq}cap(P(f,r)){\leq}\frac{k}{\sqrt{r}}$. Where k is the positive constant.

For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

In this paper, we introduce the concepts of strongly c-convex( strongly c-concave) function, almost c-convex function on preconvex spaces. We investigate the relationships between such concepts and several types of preconvex sets.

In [9], M. Green introduced the partial elimination ideals defining the multiple loci of the projection image of a closed subscheme in ${\mathbb{P}}^n$. In this paper, we give some geometric consequences obtained from partial elimination ideals.

An Einstein's connection which takes the form (2.23) is called a $^*g$-ME-connection and the corresponding vector is called a $^*g$-ME-vector. The $^*g$-ME-manifold is a generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection and we denote it by $^*g-MEX_n$. The purpose of this paper is to derive a general representation and a special representation of the $^*g$-ME-vector in $^*g-MEX_n$.

In this paper, we define the one-sided fuzzy set and we calculate the mean value and variance, defined by C. Carlsson and R. $Full{\acute{e}}r$, of this fuzzy set. And we obtain a result that, in some special case, the mean of the product of two fuzzy sets is the product of means of each fuzzy sets. This result can be considered as the similar result which is well-known in the independence of events in probability theory.

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

In this paper, we introduce a concept of a weak distance and show that AP is a bireflective subcategory of WD. Moreover, we introduce a concept of a co-tower which is an equivalent description of approach spaces.

In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.

For the pure braid groups, this paper gives a positive finite presentation whose generators are the standard Artin generators, and determines whether the submonoid generated by the Artin generators is a Garside monoid or not.

In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.

We introduce the Landau-de Gennes model in order to understand molecular structures in ferroelectric liquid crystals. We investigate equilibrium configurations of the governing energy functional by means of bifurcation analysis. In particular, we obtain periodic solutions of the functional, which is a signature of a rich variety of applications of ferroelectric materials.

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by $T_0$-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.