DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES

This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.     

TRANSFERENCE OF MAXIMAL MULTIPLIER OPERATORS ON LOCAL HARDY-LORENTZ SPACES

§1. IntroductionLet Hp(Rn), 0 < p < ∞be the Hardy spaces de?ned by Hp(Rn) = f ∈S (Rn) : sup|?t ? f| < ∞, t>0 Lp(Rn)where ? ∈S(Rn), ? = 1 and ?t(x) =     

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces e∞(△), c(△), and c0(△).Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces eτ0, eτ0, andeτ∞, respectively. The main purpose of this article is to introduce the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)) consisting of all sequences whose mth order differences are in the Euler spaces eτ0, eτc, and eτ∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)), and the Schauder basis of the spaces eτ0(△(m)), eτc(△(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space eτc(△(m)).     

PRECISE SMOOTHING EFFECTS OF HOMOGENEOUS LANDAU EQUATION IN SOBOLEV SPACES＊

In this work,we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case.We obtain a precise estimate with respect to time vari...     

ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article.a normalized biholomorphic mapping f defined on bounded starlike circular domain in C″is considered,where z=0 is a zero of order k 1 of f(z)(?) The sharp growth.covering theorems for almost starlike mappings of order a and starlile mappings of order wave established.Meanwhile,the construction of the above mappings on bounded starlike circular domain in C~n is also discussed,it provides the extremal mappings for the growth,covering theorems of the above mappings.     

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=1 xi + q j=1 yj + 2 d k=1 zk 2 = p i=1 f(xi) + q j=1 f(yj) + 2 d k=1 f(zk),where p,q,d are integers greater than 1,in non-Archimedean normed spaces.     

L-fuzzy拓扑空间中α-开运算及α-紧性

给出了L-fuzzy拓扑空间中L-fuzzyα-开运算的定义.然后借助L-fuzzyα-开运算给出L-fuzzy拓扑空间中L-fuzzyα-紧的定义;其次给出L-拓扑空间中开覆盖及fuzzyα-紧的定义;并分别得到了一些相关性质;最后讨论了L-fuzzy拓扑空间中L-fuzzyα-紧与L-拓扑空间中fuzzyα-紧之间的关系.     

L-nets and Weakly Continuous L-fuzzy Multifunctions

Ｌ－ｎｅｔｓａｎｄＷｅａｋｌｙＣｏｎｔｉｎｕｏｕｓＬ－ｆｕｚｚｙＭｕｌｔｉｆｕｎｃｔｉｏｎｓＣｈｅｎｇＪｉｓｈｕ（ＱｉｎｇｈａｉＪｕｎｉｏｒＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｘｉｎｉｎｇ８１０００７，Ｑｉｎｇｈａｉ，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔｒａｃ...     

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER CURVES＊

The basic objects of investigation in this article are nonlinear impulsive differential equations.The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-cal...     

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r（u, p）

In this paper, we introduce the sequence space er (u, p) and investigate its some topological and geometrical properties such as basis, α-, β-, γ- duals and the uniform Opial property.     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0, 1] was introduced by Martin (1980). Lin and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES

The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasi-symmetric if and only if X is not α-recurrent for all α< 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.     

Approximate Lie $\ast$-Derivations on $\rho$-complete Convex Modular algebras

In this paper, we obtain generalized Hyers--Ulam stability results of a $(m,n)$-Cauchy-Jensen functional equation associated with approximate Lie $*$-derivations on $\rho$-complete convex modular $*$-algebras $\chi_\rho$ with $\Delta_\mu$-condition on the convex modular $\rho$.     

Compactness of the Canonical Solution Operator of $ \bar \partial $ on Bounded Pseudoconvex Domains

On bounded pseudoconvex domains Ω the orthogonal projection P_q : L²_(p,q) (Ω) → ker _q is given by P_q = Id – S_{q+1 q} = Id – ^*_q+1N_{q+1 q}, where S_q is the canonical solution operator of the ‐equation and N_q is the ‐Neumann operator. We prove a formula for the solution operator S_q restricted on (0, q)‐forms with holomorphic coefficients. And as an application we get a characterization of compactness of the solution operator restricted on (0, q)‐forms with holomorphic coefficients. On general (0, q)‐forms we show that this condition is necessary for compactness of the solution operator.     

$\beta$-Homogeneous次的$F$-空间上正交可加的稳定性

在本文中我们研究了正交?程的稳定性, 其与Wlodzimierz Fechner和Justyna Sikorska在2010年得出的结果密切相关. 本文的差异性在于考虑目标空间赋予$\beta$-齐次范数和拟范数. 通过克服$\beta$-齐次范数和拟范数的瓶颈,得到了新的结果.     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近

本文研究了非线性拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象的不动点的迭代逼近问题.研究结果表明: 在任意实的Banach空间$E$中,拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象$T$~($T$不必连续)的具误差的Ishikawa与Mann迭代序列强收敛于$T$的唯一不动点.所得结果不但改进和推广了最近一些文献的相关结果,而且也改进了定理的证明方法.     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

Generalized Hankel operators and the generalized solution operator to $ \bar \partial $ on the Fock space and on the Bergman space of the unit disc

In this paper we consider Hankel operators = (Id – P ₁) from A ²(?, |z |²) to A ^2,1(?, |z |²)^⊥. Here A ²(?, |z |²) denotes the Fock space A ²(?, |z |²) = {f: f is entire and ‖f ‖² = ∫_? |f (z)|² exp (–|z |²) dλ (z) < ∞}. Furthermore A ^2,1(?, |z |²) denotes the closure of the linear span of the monomials { z ⁿ : n, l ∈ ?, l ≤ 1} and the corresponding orthogonal projection is denoted by P ₁. Note that we call these operators generalized Hankel operators because the projection P ₁ is not the usual Bergman projection. In the introduction we give a motivation for replacing the Bergman projection by P ₁. The paper analyzes boundedness and compactness of the mentioned operators. On the Fock space we show that is bounded, but not compact, and for k ≥ 3 that is not bounded. Afterwards we also consider the same situation on the Bergman space of the unit disc. Here a completely different situation appears: we have compactness for all k ≥ 1. Finally we will also consider an analogous situation in the case of several complex variables. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具$w_0$-距离度量空间中$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的最佳逼近点定理

本文提出了一类称为$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的新的非自映射,并引进了关于$\eta$的$\alpha$-逼近可容许映射和关于$\eta$的$(\alpha,d)$正则映射的概念.基于这些新概念,在$w_0$-距离度量空间中研究了此类新压缩最佳逼近点的存在唯一性,并给出了一个新的定理,推广和补充了文[Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16]和[Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]中的结果.给出了一个例子来说明主要结果的有效性.进一步地,作为推论得到关于两个映射的最佳逼近点和公共不动点定理.作为其中一个推论的应用,讨论了一类Volterra型积分方程组的求解问题.