• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.341-350
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• 2022

We introduce certain subclasses of bi-univalent functions related to the strongly Janowski functions and discuss the Taylor-Maclaurin coefficients |a₂| and |a₃| for the newly defined classes. Also, we deduce certain new results and known results as special cases of our investigation.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.537-549
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• 2022

In this paper, we consider a convex univalent function f_α,β which maps the open unit disc 𝕌 onto the vertical strip domain Ω_α,β = {w ∈ ℂ : α < ℜ < (w) < β} and introduce new subclasses of both close-to-convex and bi-close-to-convex functions with respect to an odd starlike function associated with Ω_α,β. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to these classes.

• 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.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.391-400
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• 2018

The object of this paper to construct a new class $$A^m_{{\mu},{\lambda},{\delta}}({\alpha},{\beta},{\gamma},t,{\Psi})$$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also indicated.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.677-688
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• 2018

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by $S{\breve{a}}l{\breve{a}}gean$ q-calculus operator in the open disk ${\mathbb{U}}$. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$. Some consequences of the main results are also observed.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.257-269
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• 2022

In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.215-224
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• 2019

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.331-347
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• 2022

In this paper, we introduce new subclasses of analytic and bi-univalent functions associated with the Mittag-Leffler-type Borel distribution by using the Legendre polynomials. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses. We also state certain new subclasses of Σ and initial coefficient estimates and Fekete-Szegő inequalities.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.613-621
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• 2017

In this paper, we have constructed subclasses of bi-univalent functions associated with ${\lambda}$-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coefficients for the subclasses $S^{\lambda}_{\Sigma}(k,{\alpha})$ and $S^{\lambda}_{\Sigma}(k,{\beta})$.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.629-642
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• 2022

In a recent paper, Sakar and Güney introduced a new class of bi-close-to-convex functions and determined the estimates for the general Taylor-Maclaurin coefficients of functions therein. The main purpose of this note is to give a generalization of this class. Also we point out the proof by Sakar and Güney is incorrect and present a correct proof.