共查询到20条相似文献,搜索用时 698 毫秒
1.
The present paper deals with a new modification of Baskakov operators in which the functions exp(μt) and exp(2μt), μ>0 are preserved. Approximation properties of the operators are captured, ie, uniform convergence and rate of convergence of the operators in terms of modulus of continuity, approximation behaviors of the operators exponential weighted spaces, and pointwise convergence of the operators by means of the Voronovskaya theorem. Advantages of the operators for some special functions are presented. 相似文献
2.
Çiğdem Atakut 《Numerical Functional Analysis & Optimization》2016,37(12):1488-1502
In this article, we give a generalization of the Kantorovich-Szász type operators defined by means of the Brenke type polynomials introduced in the literature and obtain convergence properties of these operators by using Korovkin’s theorem. Some graphical examples using the Maple program for this approximation are given. We also establish the order of convergence by using modulus of smoothness and Peetre’s K-functional and give a Voronoskaja type theorem. In addition, we deal with the convergence of these operators in a weighted space. 相似文献
3.
Honey Sharma 《分析论及其应用》2011,27(1):40-50
In this paper we introduce a generalization of Bernstein polynomials based on q calculus.With the help of Bohman-Korovkin type theorem,we obtain A-statistical approximation properties of these operators.Also,by using the Modulus of continuity and Lipschitz class,the statistical rate of convergence is established.We also gives the rate of A-statistical convergence by means of Peetre's type K-functional.At last,approximation properties of a rth order generalization of these operators is discussed. 相似文献
4.
Fatma Taşdelen Ali Olgun Gülen Başcanbaz-Tunca 《Proceedings Mathematical Sciences》2007,117(3):387-399
We introduce certain linear positive operators and study some approximation properties of these operators in the space of
functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of
continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence
of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using
weighted modulus of continuity. 相似文献
5.
Övgü Gürel Yılmaz Vijay Gupta Ali Aral 《Mathematical Methods in the Applied Sciences》2020,43(13):7511-7517
In this paper, we give a generalization of the Baskakov-Kantorovich type operators that reproduce functions e0 and e−x. We discuss uniform convergence of this generalization by means of the modulus of continuity and establish quantitive asymptotic formula. 相似文献
6.
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves
by a penetrable bounded obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering
problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. The
latter are typically bounded on the space of tangential vector fields of mixed regularity
T H-\frac12(divG,G){\mathsf T \mathsf H^{-\frac{1}{2}}({\rm div}_{\Gamma},\Gamma)}. Using Helmholtz decomposition, we can base their analysis on the study of pseudo-differential integral operators in standard
Sobolev spaces, but we then have to study the Gateaux differentiability of surface differential operators. We prove that the
electromagnetic boundary integral operators are infinitely differentiable without loss of regularity. We also give a characterization
of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic
scattering problem. 相似文献
7.
In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity. 相似文献
8.
J. L. Boldrini M. Poblete-Cantellano L. Friz M. A. Rojas-Medar 《Numerical Functional Analysis & Optimization》2016,37(3):304-323
The goal of this article is to present pointwise time error estimates in suitable Hilbert spaces by considering spectral Galerkin approximations of the micropolar fluid model for strong solutions. In fact, we use the properties of the Stokes and Lamé operators for prove the pointwise convergence rate in the H2-norm for the ordinary velocity and microrotational velocity and the pointwise convergence rate in the L2-norm for the time-derivative of both velocities. The novelty of our method is that we do not impose any compatibility conditions in the initial data. 相似文献
9.
Da Chun YANG 《数学学报(英文版)》2005,21(5):1209-1218
Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s(F) of Triebel and the Sobolev spaces W^1,P(F,d,μ) of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0(F) and Fpq^0(F). 相似文献
10.
Danilo Costarelli 《Numerical Functional Analysis & Optimization》2013,34(8):819-844
In this article, we study a nonlinear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to image processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L ?(? n ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L p (? n )-spaces, L αlog β L(? n )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included. 相似文献
11.
In this paper, we introduce a Durrmeyer‐type generalization of q‐Bleimann, Butzer, and Hahn operators based on q‐integers and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. We also compute rates of statistical convergence of these q‐type operators by means of the modulus of continuity and Lipschitz‐type maximal function, respectively. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present
an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder. 相似文献
13.
Rishikesh Yadav Ramakanta Meher Vishnu Narayan Mishra 《Mathematical Methods in the Applied Sciences》2019,42(18):7172-7191
In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function. 相似文献
14.
Ruchi Ruchi Nurhayat Ispir P. N. Agrawal 《Mathematical Methods in the Applied Sciences》2017,40(16):5687-5706
Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
15.
Very recently the q-Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve x 2 (2003), in this paper we modify q-Bernstein-Schurer operators to King type modification of q-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions x 2 and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators. 相似文献
16.
《Quaestiones Mathematicae》2013,36(8):1117-1133
AbstractPrior to investigating on sequence spaces and their convergence, we study the notion of statistical convergence of difference sequences of fractional order α ∈ ?. As generalizations of previous works, this study includes several special cases under different limiting conditions of α, such as the notion of statistical convergence of difference sequences of zeroth and mth (integer) order. In fact, we study certain new results on statistical convergence via the difference operator Δα and interpret them to those of previous works. Also, by using the convergence of Δα-summable sequences which is stronger than statistical convergence of difference sequences, we apply classical Bernstein operator and a generalized form of Meyer-Konig and Zeller operator to construct an example in support of our result. Also, we study the rates of Δα-statistical convergence of positive linear operators. 相似文献
17.
Manjari Sidharth Nurhayat Ispir P. N. Agrawal 《Mathematical Methods in the Applied Sciences》2017,40(11):3901-3911
This paper is in continuation of the work performed by Kajla et al. (Applied Mathematics and Computation 2016; 275 : 372–385.) wherein the authors introduced a bivariate extension of q‐Bernstein–Schurer–Durrmeyer operators and studied the rate of convergence with the aid of the Lipschitz class function and the modulus of continuity. Here, we estimate the rate of convergence of these operators by means of Peetre's K‐functional. Then, the associated generalized Boolean sum operator of the q‐Bernstein–Schurer–Durrmeyer type is defined and discussed. The smoothness properties of these operators are improved with the help of mixed K‐functional. Furthermore, we show the convergence of the bivariate Durrmeyer‐type operators and the associated generalized Boolean sum operators to certain functions by illustrative graphics using Maple algorithm. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
In this paper we present a survey of rates of pointwise approximation of modified Gamma operators Gn for locally bounded functions and absolutely continuous functions by using some inequalities and results of probability theory with the method of Bojanic-Cheng. In the paper a kind of locally bounded functions is introduced with different growth conditions in the fields of both ends of interval (0,+∞), and it is found out that the operators have different properties compared to the Gamma operators discussed in [X.M. Zeng, Approximation properties of Gamma operators, J. Math. Anal. Appl. 311 (2005) 389-401]. And we obtain two main theorems. Theorem 1 gives an estimate for locally bounded functions which subsumes the approximation of functions of bounded variation as a special case. Theorem 2 gives an estimate for absolutely continuous functions which is best possible in the asymptotical sense. 相似文献
19.
The best asymptotic constant was established by Esseen for Bernstein operators. In this paper, we extend Esseen's result to a class of linear positive operators and as byproduct we obtain the best asymptotic constant for Szász, Baskakov, Gamma, and B-Spline operators. 相似文献
20.
We use some integral operators to establish a few special properties of absolute convergence systems for l
2. 相似文献