scholarly journals On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1919
Author(s):  
Qing-Bo Cai ◽  
Reşat Aslan
Keyword(s):  
Error Estimation ◽  
Shape Parameter ◽  
Bernstein Polynomials ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Approximation Properties ◽  
Bernstein Basis ◽  
New Class ◽  
New Construction ◽  
Bernstein Basis Functions

This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.

scholarly journals A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Salma Naseer ◽  
Muhammad Abbas ◽  
Homan Emadifar ◽  
Samia Bi Bi ◽  
Tahir Nazir ◽  
...  
Keyword(s):  
Shape Control ◽  
Basis Functions ◽  
Control Parameters ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Closed Curves ◽  
Geometric Characteristics ◽  
New Class ◽  
Bernstein Basis Functions ◽  
Short Basis

In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and closed curves are also part of this study.

8-node quasi-conforming plane element by using Bernstein basis functions

2018 ◽  
Vol 70 ◽  
pp. 127-140 ◽  
Author(s):  
Changsheng Wang ◽  
Xingtong Lu ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Plane Element ◽  
Bernstein Basis Functions

scholarly journals Approximation of functions by a new class of linear operators

1972 ◽  
Vol 13 (3) ◽  
pp. 271-276 ◽  
Author(s):  
G. C. Jain
Keyword(s):  
Negative Binomial ◽  
Bernstein Polynomials ◽  
Degree Of Approximation ◽  
Linear Operators ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Approximation Of Functions ◽  
New Class ◽  
Binomial Distributions ◽  
Poisson Type

Various extensions and generalizations of Bernstein polynomials have been considered among others by Szasz [13], Meyer-Konig and Zeller [8], Cheney and Sharma [1], Jakimovski and Leviatan [4], Stancu [12], Pethe and Jain [11]. Bernstein polynomials are based on binomial and negative binomial distributions. Szasz and Mirakyan [9] have defined another operator with the help of the Poisson distribution. The operator has approximation properties similar to those of Bernstein operators. Meir and Sharma [7] and Jam and Pethe [3] deal with generalizations of Szasz-Mirakyan operator. As another generalization, we define in this paper a new operator with the help of a Poisson type distribution, consider its convergence properties and give its degree of approximation. The results for the Szasz-Mirakyan operator can easily be obtained from our operator as a particular case.

scholarly journals Decomposition of mixed pixels in MODIS data using Bernstein basis functions

2019 ◽  
Vol 13 (04) ◽  
pp. 1
Author(s):  
Yi Qin ◽  
Feng Guo ◽  
Yupeng Ren ◽  
Xin Wang ◽  
Juan Gu ◽  
...  
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Modis Data ◽  
Mixed Pixels ◽  
Bernstein Basis Functions
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