Ostrovska, SofiyaTuran, MehmetMathematics2024-07-052024-07-0520230139-99181337-221110.1515/ms-2023-00162-s2.0-85148768143https://doi.org/10.1515/ms-2023-0016https://hdl.handle.net/20.500.14411/2510The Lupa , s q-transform comes out naturally in the study of the Lupa , s 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 Lupa , s q-transform (lambda(q)f)(z), q is an element of (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f is an element of C[0, 1] have been investigated. First, the condition for a function to possess the Lupa , s 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 Lupa , s q-transform (lambda(q)f)(z) as z -> infinity are established. (c) 2023 Mathematical Institute Slovak Academy of Scienceseninfo:eu-repo/semantics/closedAccessLupas q-transformgrowth rateanalytic functionsubharmonic functionArticleQ1731177184WOS:0009362783000040