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Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
H. Tang, K. Vijaya, S. Sivasubramanian,
Published in De Gruyter Open Ltd
2021
Volume: 19

Issue: 1
Pages: 329 - 337
Abstract
Let fk (z) = z + ∑n=2k an zn be the sequence of partial sums of the analytic function f (z) = z + ∑n=2∞ an zn. In this paper, we determine sharp lower bounds for Re {f(z)/fk(z)}, Re {fk(z)/f(z)}, Re{f′(z)/fk′(z)} and Re {fk′(z)/f′(z)}, where f(z) belongs to the subclass Jp, qm (μ, α, β) of analytic functions, defined by Sǎlǎgean (p, q)-differential operator. In addition, the inclusion relations involving Nδ(e) of this generalized function class are considered. © 2021 Huo Tang et al., published by De Gruyter.