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ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
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作者 陈洁玲 刘名生 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期295-310,共16页
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,... In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors. 展开更多
关键词 Bloch-Landau type theorem Bloch constant linear complex operator harmonic mapping biharmonic mapping UNIVALENT
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On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L_2 Space
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作者 吴嘎日迪 包那 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第4期27-31, ,共5页
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates... Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) . 展开更多
关键词 linear operator smooth function class WIDTH
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On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L2 Space 被引量:2
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作者 吴嘎日迪 包那 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第4期27-31,共页
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates... Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) . 展开更多
关键词 linear operator smooth function class WIDTH
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A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES 被引量:3
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作者 王紫 王玉文 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1619-1631,共13页
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma"... In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces. 展开更多
关键词 Banach space bounded linear operator metric projection generalized inverse perturbation analysis Moore-Penrose quasi-additive
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Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings 被引量:2
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作者 李红海 谭宜家 《Northeastern Mathematical Journal》 CSCD 2007年第1期71-86,共16页
Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrice... Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized. 展开更多
关键词 antinegative commutative semiring Boolean algebra nilpotent matrix linear operator
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AN MRA YIELDS AN ORTHONORMAL WAVELET BASIS——AN OPERATOR THEORETIC PROOF 被引量:1
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作者 DAI XINGDE LU SHIJIE Department of Mathematics, UNCC, Charlotte, UN 28223, USA. Department of Applied Mathematics, Zhejiang University Hangzhou 310027 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第1期77-84,共8页
In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.
关键词 Multiresolution approximation scaling function orthonormal wavlet conjugate linear operator.
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On n-K Width of Certain Function Classes Defined by Linear Operators in L_2 Space 被引量:1
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作者 YU Rui-fang WU Ga-ridi 《Chinese Quarterly Journal of Mathematics》 2016年第1期96-101,共6页
Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give ... Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]). 展开更多
关键词 linear operator Sobolev-Orlicz class WIDTH
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On the Stable Method Computing Values of Unbounded Operators 被引量:1
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作者 Nguyen Van Kinh 《Open Journal of Optimization》 2020年第4期129-137,共9页
Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a... Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method. 展开更多
关键词 The Stable Method Ill-Posed Problem REGULARIZATION Tikhonov Method Unbounded Linear operator
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THE EXTENSION THEOREMS OF CONE LINEAR OPERATORS
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作者 盛宝怀 刘三阳 毛华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第1期71-78,共8页
A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators ... A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given. 展开更多
关键词 cone separation theorem cone linear operator extension theorem separation theorems
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RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS
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作者 Bilel KRICHEN 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期546-556,共11页
In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we es... In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter's and approximate essential spectrum. 展开更多
关键词 Demicompact linear operator relative essential spectrum Fredholm and semi-Fredholm operators measure of noncompactness.
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NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR
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作者 Muhammed ARIF Shahid MAHMOOD +1 位作者 Janusz SOKOL Jacek DZIOK 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期704-716,共13页
The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some othe... The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some other for a new subclass of analytic functions, which are defined here by means of linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. 展开更多
关键词 analytie functions SUBORDINATION functions with positive real part linear operators conic domains
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Subordination Results for p-Valent Meromorphic Functions Associated with a Linear Operator
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作者 A.O.Mostafa M.K.Aouf 《Analysis in Theory and Applications》 2014年第4期369-376,共8页
In this paper, by making use of the Hadamard products, we obtain some subordination results for certain family of meromorphic functions defined by using a new linear operator.
关键词 Meromorphic functions SUBORDINATION Hadamard product linear operator.
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ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS
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作者 方锦暄 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第10期1160-1166,共7页
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 ... 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. 展开更多
关键词 probabilistic normed space probabilistic norm of a linear operator space of operators
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On Approximation Properties of Modified Sázas-Mirakyan Operators via Jain Operators
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作者 Prashantkumar Patel Vishnu Narayan Mishra 《Analysis in Theory and Applications》 CSCD 2016年第3期232-241,共10页
In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a re... In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation and the Voronovskaya asymptotic formula. 展开更多
关键词 Positive linear operators Jain operators Szasz-Mirakyan operator.
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On the Finite-dimensional Optimal Approximations to the Infinite dimensional Linear Operators
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作者 张秀玲 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第3期96-102, ,共7页
A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exist... A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained. 展开更多
关键词 Hilbert space linear operator optimal approximation
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Some Remarks on Operators and Their Conjugates
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作者 陈滋利 张静 《Journal of Southwest Jiaotong University(English Edition)》 2010年第4期346-348,共3页
We first characterize the range spaces F for which {T':T∈K(E,F)}=K(F',E') holds for all Banach spaces E. Then we present some sufficient conditions for the equality T'=T'. Some related results are also incl... We first characterize the range spaces F for which {T':T∈K(E,F)}=K(F',E') holds for all Banach spaces E. Then we present some sufficient conditions for the equality T'=T'. Some related results are also included. 展开更多
关键词 Banach space AM-space Bounded linear operator CONJUGATE AM-compact operator
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Regularity of Continuous Linear Operators on Banach Function Spaces
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作者 JIANGNian-shengt ChenZi-li 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第1期51-56,共6页
In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.
关键词 Banach function space continuous linear operator REGULAR
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The Representation of Continuous Linear Operator by Integral
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作者 曾韧英 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第3期41-44, ,共4页
In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
关键词 Frechet space μ-integral continuous linear operator
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Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements
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作者 游宏 刘绍武 《Northeastern Mathematical Journal》 CSCD 2006年第2期219-232,共14页
Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear ... Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L : M2n(F) → M2n(F) is said to preserve the symplectic group if L(SP2n(F)) = SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X) = QPXP^-1 for any X ∈ M2n(F) or (ii) L(X) = QPX^TP^-1 for any X ∈M2n(F), where Q ∈ SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724. 展开更多
关键词 linear preserver symplectic group symplectic matrix generalized symplectic matrix linear operator
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A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation
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作者 陈湛本 石济民 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第1期29-43, ,共15页
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh... In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n). 展开更多
关键词 generalized Landau linear positive operators degree of approximation asymptotic formula
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