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Abstract and Applied Analysis
Volume 2010, Article ID 769095, 12 pages
http://dx.doi.org/10.1155/2010/769095
Research Article

A New Generating Function of () Bernstein-Type Polynomials and Their Interpolation Function

1Department of Mathematics, Faculty of Arts and Science, University of Akdeniz, 07058 Antalya, Turkey
2Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, 27310 Gaziantep, Turkey

Received 19 January 2010; Accepted 1 March 2010

Academic Editor: Lance Littlejohn

Copyright © 2010 Yilmaz Simsek and Mehmet Acikgoz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [49 citations]

The following is the list of published articles that have cited the current article.

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  • Yilmaz Simsek, Abdelmejid Bayad, and V. Lokesha, “q-Bernstein polynomials related to q-Frobenius-Euler polynomials, l-functions, and q-Stirling numbers,” Mathematical Methods in the Applied Sciences, vol. 35, no. 8, pp. 877–884, 2012. View at Publisher · View at Google Scholar
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  • Yilmaz Simsek, “Interpolation function of generalized q-Bernstein-type basis polynomials and applications,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6920, pp. 647–662, 2012. View at Publisher · View at Google Scholar
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  • Ron Goldman, Plamen Simeonov, and Yilmaz Simsek, “GENERATING FUNCTIONS FOR THE q-BERNSTEIN BASES,” Siam Journal on Discrete Mathematics, vol. 28, no. 3, pp. 1009–1025, 2014. View at Publisher · View at Google Scholar
  • Yilmaz Simsek, “Beta-type polynomials and their generating functions,” Applied Mathematics and Computation, vol. 254, pp. 172–182, 2015. View at Publisher · View at Google Scholar
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  • Serkan Araci, and Mehmet Açikgöz, “A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers,” Advances in Difference Equations, vol. 2015, no. 1, 2015. View at Publisher · View at Google Scholar
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  • Fatma Gül Gurkan, Mehmet Acıkgoz, and Erkan Agyuz, “A study on the new mixed-type polynomials related to Boole polynomials,” Afrika Matematika, 2016. View at Publisher · View at Google Scholar
  • Yilmaz Simsek, and Ahmet Yardimci, “Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and p-adic integrals,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Mehmet Acikgoz, Armen Bagdasaryan, and Serkan Araci, “On the properties of q-Bernstein-type polynomials,” Applied Mathematics and Information Sciences, vol. 11, no. 5, pp. 1259–1268, 2017. View at Publisher · View at Google Scholar
  • Erkan Agyuz, and Mehmet Acikgoz, “A note on (p,q)$(p,q)$-Bernstein polynomials and their applications based on (p,q)$(p,q)$-calculus,” Journal of Inequalities and Applications, vol. 2018, no. 1, 2018. View at Publisher · View at Google Scholar
  • Dmitry Kruchinin, Vladimir Kruchinin, and Yuriy Shablya, “Obtaining Explicit Formulas and Identities for Polynomials Defined by Generating Functions of the Form F t x ⋅ G t α,” Polynomials - Theory and Application [Working Title], 2018. View at Publisher · View at Google Scholar
  • Yilmaz Simsek, “Generating functions for unification of the multidimensional Bernstein polynomials and their applications,” Mathematical Methods in the Applied Sciences, 2018. View at Publisher · View at Google Scholar
  • Irem Kucukoglu, Buket Simsek, and Yilmaz Simsek, “Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature,” Applied Mathematics and Computation, vol. 344-345, pp. 150–162, 2019. View at Publisher · View at Google Scholar