On the -Bernstein Polynomials of Unbounded Functions with by Sofiya Ostrovska, Ahmet Yaşar Özban

“…The aim of this paper is to present new results related to the -Bernstein polynomials of unbounded functions in the case and to illustrate those results using numerical examples. …”
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A Note on the Modified q-Bernstein Polynomials by Taekyun Kim, Lee-Chae Jang, Heungsu Yi

“…We propose the modified q-Bernstein polynomials of degree n which are different q-Bernstein polynomials of Phillips (1997). …”
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On Bernstein Polynomials Method to the System of Abel Integral Equations by A. Jafarian, S. Measoomy Nia, Alireza K. Golmankhaneh, D. Baleanu

“…This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. …”
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On the Sets of Convergence for Sequences of the 𝑞-Bernstein Polynomials with 𝑞>1 by Sofiya Ostrovska, Ahmet Yaşar Özban

“…The aim of this paper is to present new results related to the convergence of the sequence of the 𝑞-Bernstein polynomials {𝐵𝑛,𝑞(𝑓;𝑥)} in the case 𝑞>1, where 𝑓 is a continuous function on [0,1]. …”
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On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals by T. Kim, J. Choi, Y. H. Kim, L. C. Jang

“…Recently, Kim's work (in press) introduced 𝑞-Bernstein polynomials which are different Phillips' 𝑞-Bernstein polynomials introduced in the work by (Phillips, 1996; 1997). …”
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On q-Euler Numbers Related to the Modified q-Bernstein Polynomials by Min-Soo Kim, Daeyeoul Kim, Taekyun Kim

“…Finally, we investigate some interesting properties of the modified q-Bernstein polynomials related to q-Euler numbers and q-Stirling numbers by using fermionic p-adic integrals on ℤp.…”
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Extracting the QCD Cutoff Parameter Using the Bernstein Polynomials and the Truncated Moments by A. Mirjalili, M. M. Yazdanpanah, Z. Moradi

“…Following that we combine the truncated Mellin moments with the Bernstein polynomials. As a result, Bernstein averages which are related to different orders of the truncated Mellin moment are obtained. …”
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Some Identities between the Extended -Bernstein Polynomials with Weight and -Bernoulli Polynomials with Weight (,) by H. Y. Lee, C. S. Ryoo

“…Using bosonic -adic -integral on , we give some interesting relationships between -Bernoulli numbers with weight (,) and -Bernstein polynomials with weight . Also, using -Bernstein polynomials with two variables, we derive some interesting properties associated with -Bernoulli numbers with weight (,).…”
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𝑞-Bernstein Polynomials Associated with 𝑞-Stirling Numbers and Carlitz's 𝑞-Bernoulli Numbers by T. Kim, J. Choi, Y. H. Kim

“…Recently, Kim (2011) introduced 𝑞-Bernstein polynomials which are different 𝑞-Bernstein polynomials of Phillips (1997). …”
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Applications of mixed finite element method based on Bernstein polynomials in numerical solution of Stokes equations by Lanyin Sun, Siya Wen

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Retracted: Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials by Abstract and Applied Analysis

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Some Relations between Twisted (h,q)-Euler Numbers with Weight α and q-Bernstein Polynomials with Weight α by N. S. Jung, H. Y. Lee, C. S. Ryoo

“…By using fermionic p-adic q-integral on ℤp, we give some interesting relationship between the twisted (h, q)-Euler numbers with weight α and the q-Bernstein polynomials.…”
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WEIERSTRASS APPROXIMATION THEOREM VIA RANDOM-SUM APPROACH by Trần Lộc Hùng

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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…The q-Bernstein polynomial-based Plateau–Bézier problem is the minimal area surface amongst all the q-Bernstein polynomial-based Bézier surfaces, spanned by the prescribed boundary. …”
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Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators by Hee Sun Jung, Ryozi Sakai

“…Lupas-type operators and Szász-Mirakyan-type operators are the modifications of Bernstein polynomials to infinite intervals. In this paper, we investigate the convergence of Lupas-type operators and Szász-Mirakyan-type operators on [0,∞).…”
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Bernstein Collocation Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations in the Most General Form by Ayşegül Akyüz-Daşcıoğlu, Neşe İşler Acar, Coşkun Güler

“…A collocation method based on the Bernstein polynomials defined on the interval [a,b] is developed for approximate solutions of the Fredholm-Volterra integrodifferential equation (FVIDE) in the most general form. …”
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Approximation Theorems for Functions of Two Variables via σ-Convergence by Mohammed A. Alghamdi

“…In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, and x2+y2 and construct an example by considering the Bernstein polynomials of two variables in support of our main result.…”
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Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0 by T. Kim, J. Choi, Y. H. Kim

“…In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated with q-Bernoulli numbers and polynomials with weight 0. …”
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Solving change of basis from Bernstein to Chebyshev polynomials by D.A. Wolfram

“…We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. …”
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Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis by Mohsen Alipour, Dumitru Baleanu, Fereshteh Babaei

“…We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. …”
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