Let A⋋(0) be a class of power series \( g(z)={\sum}_{k=0}^{\infty }{g}_k{z}^k \) such that |gk| ≤ ⋋k|g1| for all k ≥ 1, where ⋋ = (⋋k) is a sequence of positive numbers. We establish necessary and sufficient conditions that should be imposed on a function l and on an increasing sequence (np) of nonnegative integers in order to guarantee that f is an entire function whenever the Gelfond–Leont’ev–Sălăgean derivative \( {D}_{l,\left[S\right]}^{n_p}f \) and the Gelfond–Leont’ev–Ruscheweyh derivative \( {D}_{l,\left[R\right]}^{n_p}f \) belong to the class A⋋(0) for all p ∈ ℤ+ .
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 717–724, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7058.
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Sheremeta, M.M. On the Gelfond–Leont’ev–Sălăgean and Gelfond–Leont’ev–Ruscheweyh Operators and Analytic Continuation of Functions. Ukr Math J 74, 820–829 (2022). https://doi.org/10.1007/s11253-022-02103-4
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DOI: https://doi.org/10.1007/s11253-022-02103-4