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Year 2017, Volume: 5 Issue: 1, 56 - 67, 01.04.2017
https://izlik.org/JA96WB72YL

Abstract

References

  • [1] Farin, G., Curves and Surfaces for Computer AidedGeometric Design, A Practical Guide, 3rd Edition, Academic Press Inc., San Diego, 1993.
  • [2] Do Carmo, M.P., Differential Geometry Curves and Surfaces, Prentice Hall, Englewood Cliffs, 1976.
  • [3] Joy, Kenneth I. Bernstein polynomials. Visualization and Graphics Research Group Department of Computer Science University of California, 1996.
  • [4] Doha, E. H., Bhrawy A.H., Saker M.A., On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations BVP-Boundary Value Problems Vol:24 (2011), 1-16.
  • [5] Gergen, J. J., Diessel, G. and Purcell, W. H., Convergence of Extended Bernstein Polynomials in the Complex plane, Vol 13, No.4, 1963, 1171-1180.
  • [6] George M. Phillips,Bernstein Polynomials Interpolation and Approximation by Polynomials, CMS Books in Mathematics, 247-290, 2003.
  • [7] Rida T. Farouki, The Bernstein polynomial basis:a centennial retrospective Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, 2012.
  • [8] Kandasamy, W.B.V., and Smarandache, F., Dual Numbers, Zip Publishing, Ohio, 2012.
  • [9] Study, E., Die Geometrie der Dynamen, Leibzig, 1903.
  • [10] Veldkamp, G. R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanisms and Machine Theory, Vol:11 (1976), 141-156.
  • [11] Messelmi, F. Analysis of dual functions Annual Review of Chaos Theory, Bifurcations and Dynamical Systems Vol:4 (2013): 37-54.

GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS

Year 2017, Volume: 5 Issue: 1, 56 - 67, 01.04.2017
https://izlik.org/JA96WB72YL

Abstract

Bernstein polynomials are used in computer graphics for Computer Aided Geometric Design (CAGD). In this paper, we introduce the concept of the generalized dual-variable Bernstein polynomials and give its some properties. In particular, we investigate the limit and derivation equations of the dual-variable Bernstein polynomials.

References

  • [1] Farin, G., Curves and Surfaces for Computer AidedGeometric Design, A Practical Guide, 3rd Edition, Academic Press Inc., San Diego, 1993.
  • [2] Do Carmo, M.P., Differential Geometry Curves and Surfaces, Prentice Hall, Englewood Cliffs, 1976.
  • [3] Joy, Kenneth I. Bernstein polynomials. Visualization and Graphics Research Group Department of Computer Science University of California, 1996.
  • [4] Doha, E. H., Bhrawy A.H., Saker M.A., On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations BVP-Boundary Value Problems Vol:24 (2011), 1-16.
  • [5] Gergen, J. J., Diessel, G. and Purcell, W. H., Convergence of Extended Bernstein Polynomials in the Complex plane, Vol 13, No.4, 1963, 1171-1180.
  • [6] George M. Phillips,Bernstein Polynomials Interpolation and Approximation by Polynomials, CMS Books in Mathematics, 247-290, 2003.
  • [7] Rida T. Farouki, The Bernstein polynomial basis:a centennial retrospective Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, 2012.
  • [8] Kandasamy, W.B.V., and Smarandache, F., Dual Numbers, Zip Publishing, Ohio, 2012.
  • [9] Study, E., Die Geometrie der Dynamen, Leibzig, 1903.
  • [10] Veldkamp, G. R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanisms and Machine Theory, Vol:11 (1976), 141-156.
  • [11] Messelmi, F. Analysis of dual functions Annual Review of Chaos Theory, Bifurcations and Dynamical Systems Vol:4 (2013): 37-54.
There are 11 citations in total.

Details

Subjects Engineering
Journal Section Research Article
Authors

HATİCE Kuşak Samancı

Submission Date June 6, 2016
Acceptance Date December 17, 2016
Publication Date April 1, 2017
IZ https://izlik.org/JA96WB72YL
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Kuşak Samancı, H. (2017). GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS. Konuralp Journal of Mathematics, 5(1), 56-67. https://izlik.org/JA96WB72YL
AMA 1.Kuşak Samancı H. GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS. Konuralp J. Math. 2017;5(1):56-67. https://izlik.org/JA96WB72YL
Chicago Kuşak Samancı, HATİCE. 2017. “GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS”. Konuralp Journal of Mathematics 5 (1): 56-67. https://izlik.org/JA96WB72YL.
EndNote Kuşak Samancı H (April 1, 2017) GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS. Konuralp Journal of Mathematics 5 1 56–67.
IEEE [1]H. Kuşak Samancı, “GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS”, Konuralp J. Math., vol. 5, no. 1, pp. 56–67, Apr. 2017, [Online]. Available: https://izlik.org/JA96WB72YL
ISNAD Kuşak Samancı, HATİCE. “GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS”. Konuralp Journal of Mathematics 5/1 (April 1, 2017): 56-67. https://izlik.org/JA96WB72YL.
JAMA 1.Kuşak Samancı H. GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS. Konuralp J. Math. 2017;5:56–67.
MLA Kuşak Samancı, HATİCE. “GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS”. Konuralp Journal of Mathematics, vol. 5, no. 1, Apr. 2017, pp. 56-67, https://izlik.org/JA96WB72YL.
Vancouver 1.Kuşak Samancı H. GENERALIZED DUAL-VARIABLE BERNSTEIN POLYNOMIALS. Konuralp J. Math. [Internet]. 2017 Apr. 1;5(1):56-67. Available from: https://izlik.org/JA96WB72YL
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