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This article is cited in 2 scientific papers (total in 2 papers)
Real, complex and functional analysis
Partial sums of a generalized class of analytic functions defined by a generalized Srivastava–Attiya operator
K. A. Challaba, M. Darusa, F. Ghanimb a School of Mathematical Sciences,
Faculty of Science and Technology,
Universiti Kebangsaan Malaysia,
43600, Bangi-Selangor D. Ehsan, Malaysia
b Department of Mathematics,
College of Sciences,
University of Sharjah,
Sharjah, United Arab Emirates
Abstract:
Let $f_n(z)=z+\sum_{k=2}^{n} a_k z^k$ be the sequence of partial sums of the analytic function $f(z)=z+ \sum_{k=2}^{\infty} a_k z^k $. In this paper, we determine sharp lower bounds for $\Re\{f(z)/f_n(z)\}, \Re\{f_n(z)/f(z)\}, \Re\{f'(z)/f'_n(z)\}$ and $\Re\{f'_n(z)/f'(z)\} $. The efficiency of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.
Keywords:
analytic functions, Hadamard product (or convolution), generalized Hurwitz–-Lerch zeta function, Srivastava–Attiya operator.
Received December 16, 2016, published March 9, 2018
Citation:
K. A. Challab, M. Darus, F. Ghanim, “Partial sums of a generalized class of analytic functions defined by a generalized Srivastava–Attiya operator”, Sib. Èlektron. Mat. Izv., 15 (2018), 362–372
Linking options:
https://www.mathnet.ru/eng/semr924 https://www.mathnet.ru/eng/semr/v15/p362
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