Weighted Differentiation Composition Operators from Mixed-norm Spaces to Bloch-type Spaces

The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES

In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.

Essential Norms of Weighted Composition Operators from Weighted Bergman Space to Mixed-norm Space on the Unit Ball

In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.

DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF R^n

Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.

APPROXIMATION OF A CAUCHY-JENSEN ADDITIVE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.

The Gleason's problem on mixed norm spaces in convex domains

Let Ω be a bounded convex domain with C2 boundary in Cn and for given 0 ＜ p, q ≤∞ and normal weight function ψ(r) let Hp,q,ψ be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,ψ) is solvable for any fixed point a ∈Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on H-p,q,ψ.

Stability of a cubic functional equation in intuitionistic random normed spaces

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.

ON L^p-MATRICIALLY NORMED SPACES

It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.

Coefficient multipliers of mixed norm space in the ball

In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q(ψ1),Hu,v(ψ2)) for the values of p,q,u,v in three cases: (i) 0 ＜ p ≤ u ≤∞, 0 ＜ q ≤min(1,v) ≤∞. (ii) v= ∞,0 ＜ p ≤ u ≤∞, 1 ≤ u,q ≤∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤∞, and 0 ＜ p ≤ u ≤∞ or 1 ≤ p,u ≤∞. The first case extends the result of Blasco, Jevti(c), and Pavlovi(c) in one variable. The third case generalizes partly the results of Jevti(c), Jovanovi(c), and Wojtaszczyk to higher dimensions.

Rotundity of Orlicz-Bochner Space with Luxemburg Norm

In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.

A Note on the Convergence of Orlicz-Bochner Spaces with the Luxemburg Norm

In this paper, the convergence of the Orlicz-Bochner function spaces with the Luxemburg norm was proved.

Edge Enhancement for Remote Sensing Image Using Norm Algorithm in L_2 Vector Space

The Householder transformation-norm structure function in L2 vector space of linear algebra is introduced, and the edge enhancement for remote sensing images is realized. The experiment result is compared with traditional Laplacian and Sobel edge enhancements and it shows that the effect of the new method is better than that of the traditional algorithms.

NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONSIN PROBABILISTIC NORMED SPACES

The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

Solution and stability of mixed type functional equation in non-Archimedean random normed spaces

The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.

VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.

ON THE EXISTENCE OF SOLUTIONS FOR EQUATIONS WITH ACCRETIVE MAPPINGS IN PROBABILISTIC NORMED SPACES

The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.

Essential Norm of Extended Cesàro Operators between Bloch-type Spaces

The Bloch-type space Bω consists of all functions f ∈ H(B) for which||f||Bω=sup/z∈Bω(z)|▽f(z)|< ∞.Let T be the extended Ces`aro operator with holomorphic symbol . The essential norm of T as an operator from Bω to Bμ is denoted by ||T||e,B ω→Bμ . The purpose of this paper is to prove that, for ω, μ normal and ∈H(B)||T||e,B ω→Bμ■ lim sup|z|→1 μ(z)|■ (z)|∫ |z| 0 dt ω(t) .