On the Lupaş q-transform of unbounded functions
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Sofiya Ostrovska
Abstract
The Lupaş q-transform comes out naturally in the study of the Lupaş q-analogue of the Bernstein operator. It is closely related to the Heine q-distribution which has a numerous application in q-boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupaş q-transform (Λqf)(z), q ∈ (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f ∈ C[0, 1] have been investigated. First, the condition for a function to possess the Lupaş q-transform is presented. Also, results concerning the connection between growth rate of the function f(t) as t → 1− and the growth of its Lupaş q-transform (Λqf)(z) as z → ∞ are established.
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(Communicated by Gejza Wimmer)
Acknowledgement
The authors express their sincere gratitude to the anonymous referees for their valuable comments, all of which helped us to improve the paper both in terms of content and style.
References
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