• East Asian mathematical journal
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• v.37 no.3
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• pp.319-331
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• 2021

In this paper, we aim to introduce two new families of analytic and bi-univalent functions associated with the Attiya's operator, which is defined by the Hadamard product of a generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szegö problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.355-369
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• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.