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On interpolation function of the Bernstein polynomials [PDF]
, 2012 International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar, vol.
Simsek, Yilmaz
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Classification with Bernstein copula as discrimination function [PDF]
Communications in Statistics - Simulation and ComputationBernstein copula models are handy tools for constructing higher-dimensional distribution structures. This study proposes a Bernstein copula model as a discrimination function to classify the given data through the machine learning process. The dependence
Tolga Yamut, Burcu Hudaverdi Ucer
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Generalized Bernstein functions [PDF]
MATHEMATICA SCANDINAVICA, 2023 A class of functions called generalized Bernstein functions is studied. The fundamental properties of this class are given and its relation to generalized Stieltjes functions via the Laplace transform is investigated. The subclass of generalized Thorin-Bernstein functions is characterized in different ways.
Koumandos, Stamatis, Pedersen, Henrik L.
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2009
This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory.
Schilling, Rene +2 more
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This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory.
Schilling, Rene +2 more
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Generating Functions for the $q$-Bernstein Bases
SIAM Journal on Discrete Mathematics, 2014We derive explicit formulas for the generating functions of the $q$-Bernstein basis functions in terms of $q$-exponential functions. Using these explicit formulas, we derive a collection of functional equations for these generating functions which we apply to prove a variety of identities, some old and some new, for the $q$-Bernstein bases.
Ron Goldman 0002 +2 more
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Bernstein polynomials and dual functionals
Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, 2023The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.
Acu, Ana-Maria +2 more
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Approximation of Functions by a Bernstein-Type Operator
Canadian Mathematical Bulletin, 1972Various generalizations of the Bernstein operator, defined on C[0, 1] by the relation1.1wherehave been given. Note that bnk(x) is the well-known binomial distribution.
Pethe, S. P., Jain, G. C.
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Bernstein functions, complete hyperexpansivity and subnormality-II
Integral Equations and Operator Theory, 2002The notion of subnormal operator was introduced in [Summa Brasil. Math. 2, 125--134 (1950; Zbl 0041.23201)] by \textit{P. R. Halmos}, while the notion of a completely hyperexpansive operator was introduced in [Proc. Am. Math. Soc. 124, 3745--3752 (1996; Zbl 0863.47017)] by \textit{A. Athavale}.
Athavale, Ameer, Ranjekar, Abhijit
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