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Register a new userRegion of variability for certain classes of univalent functions satisfying differential inequalities
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In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of parameters.
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In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the coefficients |b0| and |b1| for functions in these new classes. Some interesting remarks and applications of the results presented here are also discussed.
In the present work, we propose to investigate the Fekete-Szego inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.
Let $mathcal{S}$ denote the family of all functions that are analytic and univalent in the unit disk $mathbb{D}:={z: |z|<1}$ and satisfy $f(0)=f^{prime}(0)-1=0$. In the present paper, we consider certain subclasses of univalent functions associated with the exponential function, and obtain the sharp upper bounds on the initial coefficients and the difference of initial successive coefficients for functions belonging to these classes.
Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. cite{HMS-AKM-PG} actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. cite{HMS-AKM-PG}, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Ali et al. cite{Ali-Ravi-Ma-Mina-class}, Srivastava et al. cite{HMS-AKM-PG} and G{u}ney et al. cite{HOG-GMS-JS-Fib-2018} in this paper, we consider certain classes of bi-univalent functions related to shell-like curves connected with Fibonacci numbers to obtain the estimates of second, third Taylor-Maclaurin coefficients and Fekete - Szeg{o} inequalities. Further, certain special cases are also indicated. Some interesting remarks of the results presented here are also discussed.
A starlike univalent function $f$ is characterized by the function $zf(z)/f(z)$; several subclasses of these functions were studied in the past by restricting the function $zf(z)/f(z)$ to take values in a region $Omega$ on the right-half plane, or, equivalently, by requiring the function $zf(z)/f(z)$ to be subordinate to the corresponding mapping of the unit disk $mathbb{D}$ to the region $Omega$. The mappings $w_1(z):=z+sqrt{1+z^2}, w_2(z):=sqrt{1+z}$ and $w_3(z):=e^z$ maps the unit disk $mathbb{D}$ to various regions in the right half plane. For normalized analytic functions $f$ satisfying the conditions that $f(z)/g(z), g(z)/zp(z)$ and $p(z)$ are subordinate to the functions $w_i, i=1,2,3$ in various ways for some analytic functions $g(z)$ and $p(z)$, we determine the sharp radius for them to belong to various subclasses of starlike functions.
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