This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption...This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.展开更多
In this paper,we study the reiterated homogenization operators Lε=-div(A(x/ε,x/ε^(2))∇).We establish the homogenized problem and representation equa-tion by introducing the two correctors.As a consequence,we obtain...In this paper,we study the reiterated homogenization operators Lε=-div(A(x/ε,x/ε^(2))∇).We establish the homogenized problem and representation equa-tion by introducing the two correctors.As a consequence,we obtain the H10 and L2 convergence estimates of solutions.展开更多
In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its c...In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.展开更多
L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is prove...L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is proved to hold for very general measures.展开更多
In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the dir...In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the direct approximationtheorem.展开更多
In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the co...In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.展开更多
We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also consid...We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith＇s celebrated work （Journal of Functional Analysis 205 （2003） 62-89）. The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping.展开更多
In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （...In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.展开更多
For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x±...For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.展开更多
The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of conv...The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of convergence by using the modulus of continuity. Finally, we obtain the degree of approximation by means of Lipschitz type class.展开更多
Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scal...Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scaling factors.Consequently,our method offers an alternative to the existing fractal interpolation functions(FIFs).We construct a sequence of-FIFs using a suitable sequence of iterated function systems(IFSs).Without imposing any condition on the scaling vector,we establish constrained interpolation by using fractal functions.In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data.The existence of Cr--FIFs is investigated.We identify suitable conditions on the associated scaling factors so that-FIFs preserve r-convexity in addition to the Cr-smoothness of original function.展开更多
Asymptotic and Partial Asymptotic Hankel Operators on H^2(D^n)Anuradha GUPTA Bhawna GUPTA Abstract In this paper,we generalize the concept of asymptotic Hankel operators on H^2(D)to the Hardy space H^2(D^n)(over polyd...Asymptotic and Partial Asymptotic Hankel Operators on H^2(D^n)Anuradha GUPTA Bhawna GUPTA Abstract In this paper,we generalize the concept of asymptotic Hankel operators on H^2(D)to the Hardy space H^2(D^n)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.展开更多
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10671211)Hunan Provincial Natural Science Foundation of China (Grant No. 06JJ20046)the Natural Science Foundation of Education Department of Hunan Province in China (Grant No. 06C461)
文摘This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.
基金Supported by National Natural Science Foundation of China(Grant Nos.11861045,11626239 and 11701449)China Scholarship Council(Grant No.201708410483)Education Department of Henan Province(Grant No.18A110037).
文摘In this paper,we study the reiterated homogenization operators Lε=-div(A(x/ε,x/ε^(2))∇).We establish the homogenized problem and representation equa-tion by introducing the two correctors.As a consequence,we obtain the H10 and L2 convergence estimates of solutions.
文摘In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.
文摘L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is proved to hold for very general measures.
基金Supported by the Zhejiang Provincial Natural Science Foundation
文摘In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the direct approximationtheorem.
基金Project supported by Scientific Research Fund of Chongqing Municipal Education Commission (kj0604-16)
文摘In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.
基金Supported by the Natural Science Foundation of Yunnan Province (Grant No.2009ZC013X)Basic Research Foundation of Education Bureau of Yunnan Province (Grant No.09Y0079)
文摘We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith＇s celebrated work （Journal of Functional Analysis 205 （2003） 62-89）. The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping.
文摘In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.
文摘For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.
文摘The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of convergence by using the modulus of continuity. Finally, we obtain the degree of approximation by means of Lipschitz type class.
基金Supported by Council of Scienti c&Industrial Research(CSIR),India(25(0290)/18/EMR-II).
文摘Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scaling factors.Consequently,our method offers an alternative to the existing fractal interpolation functions(FIFs).We construct a sequence of-FIFs using a suitable sequence of iterated function systems(IFSs).Without imposing any condition on the scaling vector,we establish constrained interpolation by using fractal functions.In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data.The existence of Cr--FIFs is investigated.We identify suitable conditions on the associated scaling factors so that-FIFs preserve r-convexity in addition to the Cr-smoothness of original function.
文摘Asymptotic and Partial Asymptotic Hankel Operators on H^2(D^n)Anuradha GUPTA Bhawna GUPTA Abstract In this paper,we generalize the concept of asymptotic Hankel operators on H^2(D)to the Hardy space H^2(D^n)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.
