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CONVOLUTION PROPERTIES FOR ANALYTIC FUNCTIONS DEFINED BY q-DIFFERENCE OPERATOR
Asena Cetinkaya,Arzu Yemis ci S en,Yasar Polatoglu 호남수학회 2018 호남수학학술지 Vol.40 No.4
In this paper, we de ned new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coe cient estimates for both classes q-Spirallike and q-Robertson functions denoted by Sq [A;B] and Cq [A;B], respectively.
CONVOLUTION PROPERTIES FOR ANALYTIC FUNCTIONS DEFINED BY q-DIFFERENCE OPERATOR
Cetinkaya, Asena,Sen, Arzu Yemisci,Polatoglu, Yasar The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.4
In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.
On spirallike functions related to bounded radius rotation
Asena Cetinkaya,Hakan Mete Tastan 호남수학회 2022 호남수학학술지 Vol.44 No.1
In the present paper, we prove the growth and distortion theorems for the spirallike functions class $\mathcal{S}_k(\lambda)$ related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class $\mathcal{S}_k(\lambda)$. Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.
Spirallike and Robertson Functions of Complex Order with Bounded Boundary Rotations
Ahuja, Om,Cetinkaya, Asena,Kahramaner, Yasemin Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.2
Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.
Om Ahuja,Nisha Bohra,Asena Cetinkaya,Sushil Kumar 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szeg¨o inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.
Ahuja, Om P.,Cetinkaya, Asena,Bohra, Nisha The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.
Analytic functions with conic domains associated with certain generalized $q$-integral operator
OM P. AHUJA,Asena Cetinkaya,Naveen Kumar Jain 대한수학회 2023 대한수학회논문집 Vol.38 No.4
In this paper, we define a new subclass of $k$-uniformly starlike functions of order $\gamma~ (0\leq\gamma<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szeg\"{o} inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $\gamma$ by using the generalized $q$-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.