On the eigenfunctions of the <i>q</i>-Bernstein operators

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On the eigenfunctions of the AnnalFuncAnal_2023_SO_MehmetTuran.pdf (293 KB)

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2023

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Springer Basel Ag

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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The eigenvalue problems for linear operators emerge in various practical applications in physics and engineering. This paper deals with the eigenvalue problems for the q-Bernstein operators, which play an important role in the q-boson theory of modern theoretical physics. The eigenstructure of the classical Bernstein operators was investigated in detail by S. Cooper and S. Waldron back in 2000. Some of their results were extended for other Bernstein-type operators, including the q-Bernstein and the limit q-Bernstein operators. The current study is a pursuit of this research. The aim of the present work is twofold. First, to derive for the q-Bernstein polynomials analogues of the Cooper-Waldron results on zeroes of the eigenfunctions. Next, to present in detail the proof concerning the existence of non-polynomial eigenfunctions for the limit q-Bernstein operator.

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Ostrovska, Sofiya/0000-0003-1842-7953
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Ostrovska, Sofiya ORCID logo

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Eigenvalue, Eigenfunction, Infinite linear system, q-Bernstein operator

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Q2

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14

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1

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https://doi.org/10.1007/s43034-022-00235-z
 https://hdl.handle.net/20.500.14411/2394

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