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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- RNDr. Stanislav Jakubec, DrSc. passed away
- Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
- Conditions forcing the existence of relative complements in lattices and posets
- Radically principal MV-algebras
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- Padovan or Perrin numbers that are concatenations of two distinct base b repdigits
- Addendum to “A generalization of a result on the sum of element orders of a finite group”
- Remarks on w-distances and metric-preserving functions
- Solution of logarithmic coefficients conjectures for some classes of convex functions
- Multiple periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian and partially periodic potentials
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- Fourier transform inversion: Bounded variation, polynomial growth, Henstock–Stieltjes integration
- (ε, A)-approximate numerical radius orthogonality and numerical radius derivative
- Wg-Drazin-star operator and its dual
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- K-contact and (k, μ)-contact metric as a generalized η-Ricci soliton
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