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Опубліковано: 23 лютого 2024

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Статті в журналах з теми "BERNSTEIN OPERATOR"

1

Ong, Seng Huat, Choung Min Ng, Hong Keat Yap, and Hari Mohan Srivastava. "Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators." Axioms 11, no. 10 (October 8, 2022): 537. http://dx.doi.org/10.3390/axioms11100537.

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Анотація:
The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney–Sharma operator is the Szász–Mirakyan operator averaged by a certain probability distribution.
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2

Ostrovska, Sofiya. "A Survey of Results on the Limit -Bernstein Operator." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/159720.

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The limit -Bernstein operator emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the -operators. Over the past years, the limit -Bernstein operator has been studied widely from different perspectives. It has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit -Bernstein operator related to the approximation theory. A complete bibliography is supplied.
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3

Kajla, Arun, and Dan Miclǎuş. "Modified Bernstein–Durrmeyer Type Operators." Mathematics 10, no. 11 (May 30, 2022): 1876. http://dx.doi.org/10.3390/math10111876.

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Анотація:
We constructed a summation–integral type operator based on the latest research in the linear positive operators area. We establish some approximation properties for this new operator. We highlight the qualitative part of the presented operator; we studied uniform convergence, a Voronovskaja-type theorem, and a Grüss–Voronovskaja type result. Our subsequent study focuses on a direct approximation theorem using the Ditzian–Totik modulus of smoothness and the order of approximation for functions belonging to the Lipschitz-type space. For a complete image on the quantitative estimations, we included the convergence rate for differential functions, whose derivatives were of bounded variations. In the last section of the article, we present two graphs illustrating the operator convergence.
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4

Gonska, Heiner, Ioan Raşa, and Elena-Dorina Stănilă. "Lagrange-type operators associated with Uan." Publications de l'Institut Math?matique (Belgrade) 96, no. 110 (2014): 159–68. http://dx.doi.org/10.2298/pim1410159g.

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Анотація:
We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein-Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the derivatives of the operator images are included. Our main tool is the eigenstructure of the members of the class.
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5

Finta, Zoltán. "Approximation properties of (p, q)-Bernstein type operators." Acta Universitatis Sapientiae, Mathematica 8, no. 2 (December 1, 2016): 222–32. http://dx.doi.org/10.1515/ausm-2016-0014.

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Анотація:
AbstractWe introduce a new generalization of the q-Bernstein operators involving (p, q)-integers, and we establish some direct approximation results. Further, we define the limit (p, q)-Bernstein operator, and we obtain its estimation for the rate of convergence. Finally, we introduce the (p, q)-Kantorovich type operators, and we give a quantitative estimation.
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6

ACU, ANA MARIA, and P. N. AGRAWAL. "Better approximation of functions by genuine Bernstein-Durrmeyer type operators." Carpathian Journal of Mathematics 35, no. 2 (2019): 125–36. http://dx.doi.org/10.37193/cjm.2019.02.01.

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Анотація:
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.
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7

Finta, Zoltan. "A generalization of the Lupaș \(q\)-analogue of the Bernstein operator." Journal of Numerical Analysis and Approximation Theory 45, no. 2 (December 9, 2016): 147–62. http://dx.doi.org/10.33993/jnaat452-1090.

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Анотація:
We introduce a Stancu type generalization of the Lupaș \(q\)-analogue of the Bernstein operator via the parameter \(\alpha\). The construction of our operator is based on the generalization of Gauss identity involving \(q\)-integers. We establish the convergence of our sequence of operators in the strong operator topology to the identity, estimating the rate of convergence by using the second order modulus of smoothness. For \(\alpha\) and \(q\) fixed, we study the limit operator of our sequence of operators taking into account the relationship between two consecutive terms of the constructed sequence of operators.
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8

Özger, Faruk, Ekrem Aljimi, and Merve Temizer Ersoy. "Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators." Mathematics 10, no. 12 (June 11, 2022): 2027. http://dx.doi.org/10.3390/math10122027.

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Анотація:
An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters λ, α and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.
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9

Özalp Güller, Özge, Ecem Acar, and Sevilay Kırcı Serenbay. "Nonlinear Bivariate Bernstein–Chlodowsky Operators of Maximum Product Type." Journal of Mathematics 2022 (August 8, 2022): 1–11. http://dx.doi.org/10.1155/2022/4742433.

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Анотація:
The positive nonlinear operators with maximum and product were introduced by Bede. In this study, nonlinear maximum product type of bivariate Bernstein–Chlodowsky operators is defined and the approximation properties are investigated with the help of new definitions. In this paper, it was aimed that the order of approximation obtained with the nonlinear maximum product type of operator sequences would be better than the degree of approximation of the known linear operator sequences.
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10

Usta, Fuat, Mohammad Mursaleen, and İbrahim Çakır. "Approximation properties of Bernstein-Stancu operators preserving e−2x." Filomat 37, no. 5 (2023): 1523–34. http://dx.doi.org/10.2298/fil2305523u.

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Анотація:
Bernstein-Stancu operators are one of the most powerful tool that can be used in approximation theory. In this manuscript, we propose a new construction of Bernstein-Stancu operators which preserve the constant and e?2x, x > 0. In this direction, the approximation properties of this newly defined operators have been examined in the sense of different function spaces. In addition to these, we present the Voronovskaya type theorem for this operators. At the end, we provide two computational examples to demonstrate that the new operator is an approximation procedure.
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Дисертації з теми "BERNSTEIN OPERATOR"

1

Cripps, Robert J. "Trend identification and the Bézier-Bernstein Operator." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/26973.

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Анотація:
The techniques for identifying or describing the trend of data sequences generally rely on fitting either globally or locally piecewise, a low order polynomial to the observations. For data sequences containing trend with random and/or oscillatory movement the choice of the trend descriptor relies more on experience than technique.
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2

Stanila, Elena Dorina [Verfasser], Heinz H. [Akademischer Betreuer] Gonska, and Margareta [Akademischer Betreuer] Heilmann. "On Bernstein-Euler-Jacobi Operators / Elena Dorina Stanila. Gutachter: Margareta Heilmann. Betreuer: Heinz H. Gonska." Duisburg, 2014. http://d-nb.info/1058323482/34.

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3

Wu, Hsi-Chun, and 吳希淳. "Asymptotic Behavior of Dual Functionals to the Bernstein Operator." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/89238281996655972817.

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Анотація:
碩士
輔仁大學
數學系研究所
98
The Bernstein operator Bn has an eigenstructure with positive eigenvalues and corresponding monic eigenfunctions of polynomials. The dual functionals μ^(n)_k acting on C[0, 1] associated with Bn can be represented explicitly. An observation of a symmetric property of dual functionals can be verified easily. In this research, we mainly prove that the boundedness of the sequence {||μ^(n)_k||}^∞_{n=0} is a necessary and sufficient condition for μ^(n)_k (f) being convergent to some μ^∗_k(f) for every f in C[0, 1].
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Книги з теми "BERNSTEIN OPERATOR"

1

Gal, Sorin G. Approximation by complex Bernstein and convolution type operators. Singapore: World Scientific, 2009.

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2

Bustamante, Jorge. Bernstein Operators and Their Properties. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0.

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3

Bustamante, Jorge. Bernstein Operators and Their Properties. Birkhäuser, 2018.

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4

Bustamante, Jorge. Bernstein Operators and Their Properties. Birkhäuser, 2017.

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5

Cripps, R. J. Trend identification and the Bezier-Bernstein operator. 1986.

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6

Gal, Sorin G. Approximation by Complex Bernstein and Convolution Type Operators. World Scientific Publishing Co Pte Ltd, 2009.

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7

Rhomari, Noureddine. On Bernstein Type and Maximal Inequalities for Dependent Banach-Valued Random Vectors and Applications. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.14.

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Анотація:
This article discusses some results on Bernstein type and maximal inequalities for partial sums of dependent random vectors taking their values in separable Hilbert or Banach spaces of finite or infinite dimension. Two types of measure of dependence are considered: strong mixing coefficients (α-mixing) and absolutely regular mixing coefficients (β-mixing). These inequalities, which are similar to those in the dependent real case, are used to derive the strong law of large numbers (SLLN) and the bounded law of the iterated logarithm (LIL) for absolutely regular Hilbert- or Banach-valued processes under minimal mixing conditions. The article first introduces the relevant notation and definitions before presenting the maximal inequalities in the strong mixing case, followed by the absolutely regular mixing case. It concludes with some applications to the SLLN, the bounded LIL for Hilbertian or Banachian absolutely regular processes, the recursive estimation of probability density, and the covariance operator estimations.
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Частини книг з теми "BERNSTEIN OPERATOR"

1

Aral, Ali, Vijay Gupta, and Ravi P. Agarwal. "q-Bernstein-Type Integral Operators." In Applications of q-Calculus in Operator Theory, 113–44. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6946-9_4.

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2

Cavaretta, A. S., and A. Sharma. "Variation diminishing properties and convexity for the tensor product Bernstein operator." In Functional Analysis and Operator Theory, 18–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0093794.

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3

Hernández, F. L., Y. Raynaud, and E. M. Semenov. "Bernstein Widths and Super Strictly Singular Inclusions." In A Panorama of Modern Operator Theory and Related Topics, 359–76. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0221-5_15.

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4

Franz, Uwe, and René Schott. "Gauss laws in the sense of Bernstein on quantum groups." In Stochastic Processes and Operator Calculus on Quantum Groups, 161–81. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9277-2_8.

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5

Jayasri, C., and Y. Sitaraman. "On a Bernstein-Type Operator of Bleimann, Butzer and Hahn III." In Approximation, Probability, and Related Fields, 297–301. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4615-2494-6_22.

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6

Bustamante, Jorge. "Bernstein-Type Inequalities." In Bernstein Operators and Their Properties, 273–94. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0_5.

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7

Bustamante, Jorge. "Iterates of Bernstein Polynomials." In Bernstein Operators and Their Properties, 359–69. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0_8.

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8

Bustamante, Jorge. "Basic Properties of Bernstein Operators." In Bernstein Operators and Their Properties, 75–160. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0_2.

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9

Bustamante, Jorge. "Bernstein Polynomials as Linear Operators." In Bernstein Operators and Their Properties, 161–73. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0_3.

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10

Bustamante, Jorge. "Linear Combinations of Bernstein Polynomials." In Bernstein Operators and Their Properties, 371–95. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55402-0_9.

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Тези доповідей конференцій з теми "BERNSTEIN OPERATOR"

1

Zapryanova, Teodora, and Gancho Tachev. "Approximation by the iterates of Bernstein operator." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766784.

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2

Esi, Ayhan, Nagarajan Subramanian, and M. Kemal Ozdemir. "Triple sequence spaces of intuitionistic rough I-convergence defined by compact Bernstein operator." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136144.

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3

Chutchavong, V., P. Tharaphimaan, T. Anuwongpinit, B. Purahong, and K. Janchitrapongvej. "Low pass filters based on bernstein-balazs operators." In the 3rd International Conference. New York, New York, USA: ACM Press, 2017. http://dx.doi.org/10.1145/3162957.3163021.

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4

Wang, Peng-Hui, та Qing-Bo Cai. "Statistical approximation properties of Stancu type λ-Bernstein operators". У 2019 IEEE 2nd International Conference on Electronic Information and Communication Technology (ICEICT). IEEE, 2019. http://dx.doi.org/10.1109/iceict.2019.8846309.

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5

Lian, Bo-yong, та Qing-bo Cai. "The Bézier variant of a new type λ–Bernstein operators". У 2019 6th International Conference on Information Science and Control Engineering (ICISCE). IEEE, 2019. http://dx.doi.org/10.1109/icisce48695.2019.00126.

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6

Pandey, Rajesh K., and Om P. Agrawal. "Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12388.

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Анотація:
This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.
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7

Zhao, Yi, and Long Chen. "Weighted approximation of functions by Bernstein operators on the semi axis." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002673.

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8

Cai, Qing-Bo. "Convergence of Modification of the Kantorovich-Type q-Bernstein-Stancu-Schurer Operators." In 2016 6th International Conference on Digital Home (ICDH). IEEE, 2016. http://dx.doi.org/10.1109/icdh.2016.064.

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9

Coroianu, Lucian, Sorin G. Gal, and Barnabas Bede. "Approximation of fuzzy numbers by nonlinear Bernstein operators of max-product kind." In 7th conference of the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.61.

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10

Zhao, Yi. "A converse theorem on weighted approximation of functions with singularities by Bernstein operators." In 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet). IEEE, 2011. http://dx.doi.org/10.1109/cecnet.2011.5768405.

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