scholarly journals Coefficient Estimates for Certain Subclasses of Biunivalent Functions Defined by Convolution

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
R. Vijaya ◽  
T. V. Sudharsan ◽  
S. Sivasubramanian
Keyword(s):  
Function Class ◽  
Coefficient Estimates ◽  
Open Disc

We introduce two new subclasses of the function class Σ of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients a2 and a3 for the two subclasses are obtained. Moreover, we verify Brannan and Clunie’s conjecture a2≤2 for our subclasses.

scholarly journals Starlike functions of complex order involving q-hypergeometric functions with fixed point

2014 ◽  
Vol 13 (1) ◽  
pp. 51-63
Author(s):  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Murugesan Kasthuri
Keyword(s):  
Fixed Point ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Function Class ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Open Disc ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractRecently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals Certain Subclasses of Bistarlike and Biconvex Functions Based on Quasi-Subordination

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Nanjundan Magesh ◽  
Vitalrao Kupparao Balaji ◽  
Jagadesan Yamini
Keyword(s):  
Function Class ◽  
Coefficient Estimates

We introduce the unified biunivalent function classMq,σδ,λ(γ,φ)defined based on quasi-subordination and obtained the coefficient estimates for Taylor-Maclaurin coefficients|a2|and|a3|. Several related classes of functions are also considered and connections to earlier known and new results are established.

scholarly journals Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem
Keyword(s):  
Linear Combination ◽  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Faber Polynomials ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class

In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HORADAM POLYNOMIAL

2020 ◽  
Vol 9 (12) ◽  
pp. 10091-10102
Author(s):  
D. Kavitha ◽  
K. Dhanalakshmi ◽  
N. Arulmozhi
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Univalent Function ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Novel ◽  
Coefficient Estimates

In this present article, we studied and examined the novel general subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the Horadam polynomial. This study locates estimates on the Taylor - Maclaurin coefficients $|a_{2}|$ {\it and} $|a_{3}|$ in functions of the class which are considered. Additionally, Fekete-Szeg\"{o} inequality of functions belonging to this subclasses are also obtained.

scholarly journals Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1888
Author(s):  
S. Melike Aydoğan ◽  
Zeliha Karahüseyin
Keyword(s):  
Univalent Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Coefficient Bounds ◽  
Special Cases

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

scholarly journals Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 418 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
Teodor Bulboacă ◽  
Bassant M. El-Matary
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

scholarly journals A study of the Fekete-Szegö functional and coefficient estimates for subclasses of analytic functions satisfying a certain subordination condition and associated with the Gegenbauer polynomials

2021 ◽  
Vol 7 (2) ◽  
pp. 2568-2584
Author(s):  
H. M. Srivastava ◽  
◽  
Muhammet Kamalı ◽  
Anarkül Urdaletova ◽  
◽  
...  
Keyword(s):  
Chebyshev Polynomials ◽  
Analytic Functions ◽  
Function Class ◽  
Gegenbauer Polynomials ◽  
Coefficient Estimates ◽  
Ultraspherical Polynomials

<abstract><p>In this paper, we introduce and study a new subclass of normalized analytic functions, denoted by</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathcal F_{\left(\beta,\gamma\right)} \bigg(\alpha,\delta,\mu,H\big(z,C_{n}^{\left(\lambda \right)} \left(t\right)\big)\bigg), $\end{document} </tex-math></disp-formula></p> <p>satisfying the following subordination condition and associated with the Gegenbauer (or ultraspherical) polynomials $ C_{n}^{\left(\lambda\right)}(t) $ of order $ \lambda $ and degree $ n $ in $ t $:</p> <p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \alpha \left(\frac{zG^{'}\left(z\right)}{G\left(z\right)} \right)^{\delta}+\left(1-\alpha\right)\left(\frac{zG^{'} \left(z\right)}{G\left(z\right)}\right)^{\mu} \left(1+\frac{zG^{''}\left(z\right)}{G^{'} \left(z\right)} \right)^{1-\mu} \prec H\big(z,C_{n}^{\left(\lambda\right)} \left(t\right)\big), $\end{document} </tex-math></disp-formula></p> <p>where</p> <p><disp-formula> <label/> <tex-math id="FE3"> \begin{document}$ H\big(z,C_{n}^{\left(\lambda\right)}\left(t\right)\big) = \sum\limits_{n = 0}^{\infty} C_n^{(\lambda)}(t)\;z^n = \left(1-2tz+z^2\right)^{-\lambda}, $\end{document} </tex-math></disp-formula></p> <p><disp-formula> <label/> <tex-math id="FE4"> \begin{document}$ G\left(z\right) = \gamma \beta z^{2} f^{''} \left(z\right)+\left(\gamma-\beta \right)zf^{'} \left(z\right)+\left(1-\gamma+\beta\right)f\left(z\right), $\end{document} </tex-math></disp-formula></p> <p>$ 0\leqq \alpha \leqq 1, $ $ 1\leqq \delta \leqq 2, $ $ 0\leqq \mu \leqq 1, $ $ 0\leqq \beta \leqq \gamma \leqq 1 $, $ \lambda \geqq 0 $ and $ t\in \left(\frac{1}{\sqrt{2}}, 1\right] $. For functions in this function class, we first derive the estimates for the initial Taylor-Maclaurin coefficients $ \left|a_{2}\right| $ and $ \left|a_{3}\right| $ and then examine the Fekete-Szegö functional. Finally, the results obtained are applied to subclasses of normalized analytic functions satisfying the subordination condition and associated with the Legendre and Chebyshev polynomials. The basic or quantum (or $ q $-) calculus and its so-called trivially inconsequential $ (p, q) $-variations have also been considered as one of the concluding remarks.</p></abstract>

scholarly journals Maclaurin Coefficient Estimates for New Subclasses of Bi-univalent Functions Connected with a q-Analogue of Bessel Function

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Sheza M. El-Deeb
Keyword(s):  
Bessel Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce new subclasses of the function class Σ of bi-univalent functions connected with a q-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients a2 and a3 for functions in these new subclasses.

Coefficient estimates for Libera type bi-close-to-convex functions

2021 ◽  
Vol 71 (6) ◽  
pp. 1401-1410
Author(s):  
Serap Bulut
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Coefficient Estimates

Abstract In a very recent paper, Wang and Bulut [A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876–880] determined the estimates for the general Taylor-Maclaurin coefficients of functions belonging to the bi-close-to-convex function class. In this study, we introduce the class of Libera type bi-close-to-convex functions and obtain the upper bounds for the coefficients of functions belonging to this class. Our results generalize the results in the above mentioned paper.

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