Geometric Properties of the Lupas <i>q</I>-transform

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2014

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Tusi Mathematical Research Group

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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 Lupas q-transform emerges in the study of the limit q-Lupas operator. This transform is closely connected to the theory of positive linear operators of approximation theory, the q-boson operator calculus, the methods of summation of divergent series, and other areas. Given q is an element of (0, 1), f is an element of C[0, 1], the Lupas q-transform of f is defined by: [GRAPHICS] where [GRAPHICS] The analytical and approximation properties of A(q) have already been examined. In this paper, some properties of the Lupas q-transform related to continuous linear operators in normed linear spaces are investigated.

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Lupas q-transform, Bernstein operator, continuous linear operator, isomorphic embedding

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8

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2

Start Page

139

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145

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https://doi.org/10.15352/bjma/1396640059
 https://hdl.handle.net/20.500.14411/122

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