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Regularity of discrete multisublinear fractional maximal functions

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Science China Mathematics 2017年第8期60卷 1461-1476页

作者： LIU Feng WU HuoXiong College of Mathematics and Systems Science Shandong University of Science and Technology School of Mathematical Sciences Xiamen University

We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered *** prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on ***,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also *** applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.

关键词： discrete multisublinear fractional maximal operator discrete fractional maximal operator bounded variation continuity

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Banach空间中有界变差集值函数的性质

哈尔滨工业大学学报 1991年第3期 102-105+107页

作者：薛小平张波哈尔滨工业大学数学系

In recent years, there has been increasing interest in set-valued functions because of their importance in several applied areas of research, such as mathematics economics, optimization and optimal control and statist... 详细信息

关键词： Set-valued function bounded variation

MEROMORPHIC FUNCTIONS WITH bounded BOUNDARY ROTATION

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Acta Mathematica Scientia 2014年第2期34卷 466-472页

作者： Jacek DZIOK Faculty of Mathematics and Natural Sciences University of Rzeszów

In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.

关键词： Meromorphic functions bounded variation bounded boundary rotation

On the rate of convergence of two generalized Bernstein type operators

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Applied Mathematics(A Journal of Chinese Universities) 2020年第3期35卷 321-331页

作者： LIAN Bo-yong CAI Qing-bo Department of Mathematics Yang-En UniversityQuanzhou 362014China School of Mathematics and Computer Science Quanzhou Normal UniversityQuanzhou 362000China

In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type *** establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of *** means of construction of suitable functions and the method of Bojanic and Cheng,we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.

关键词： Bernstein operators modulus of smoothness rate of convergence bounded variation

Continuity of Hardy-Littlewood Maximal Function

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 982-990页

作者： Di WU Dun-yan YAN School of Science Zhejiang University of Science and TechnologyHangzhou 310023China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China

In the paper,we characterize a necessary and sufficient condition which ensures the continuities of the non-centered Hardy-Lit tiewood maximal function Mf and the centered Hardy-Lit tiewood maximal function Mcf on R^*** two applications,we can easily deduce that Mcf and Mf are continuous if f is continuous,and Mf is continuous if f is of local bounded variation on R.

关键词： Hardy-Littlewood maximal function bounded variation continuity

variationAL IMAGE FUSION WITH FIRST AND SECOND-ORDER GRADIENT INFORMATION

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Journal of Computational Mathematics 2016年第2期34卷 200-222页

作者： Fang Li Tieyong Zeng Department of Mathematics East China Normal University and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.

关键词： Image fusion Feature selection bounded variation Second bounded variation,Split Bregman

ON CONVERGENCE OF GENERAL GAMMA TYPE OPERATORS

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Analysis in Theory and Applications 2011年第3期27卷 288-300页

作者： Harun Karsli Abant Izzet Baysal University

The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of p... 详细信息

关键词： rate of convergence gamma operator bounded variation total variation

IMPROVED RATE OF CONVERGENCE FOR THE MODIFIED SZASZ-MIRAKYAN OPERATORS

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Analysis in Theory and Applications 2000年第3期16卷 94-99页

作者： Gupta Vijay Gupta Prabhakar Rogalski Marc Division of Applied Science(Mathematics) Netagji Subhas Institute of TechnologyAzad Hind Fauj Marg Sector 3Owarka110045New DelhiIndia Equipe D'Analyse Universite Pierre et Marie Curie-Paris 6Tour 46-Case 186-4Place JussienF-75252Paris Cedex 05France

For some locally bounded function f measurable on the interval [0,∞) we have estimated the rate of convergence of the modified Szasz-Mirakyan operators Mnf at those points x∈[0,∞) at which one sided limits f(±) exist. We have used the Chanturiya's modulus of variation. Our result improves the estimate of [1], [3], [4], [5], [6] and [9].

关键词： Type Operator bounded variation Auxiliary Function Improve Rate Auxiliary Result

Fractal dimensions of fractional calculus of fractal functions

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Fractal dimensions of fractional calculus of fractal functio...