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Register a new userInitial successive coefficients for certain classes of univalent functions involving the exponential function
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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.
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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 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.
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.
In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $kappa-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third coefficients) and Fekete - Szeg{o} inequalities. Also we discuss the special cases of the obtained results.
Let $es$ be the class of analytic and univalent functions in the unit disk $|z|<1$, that have a series of the form $f(z)=z+ sum_{n=2}^{infty}a_nz^n$. Let $F$ be the inverse of the function $fines$ with the series expansion %in a disk of radius at least $1/4$ $F(w)=f^{-1}(w)=w+ sum_{n=2}^{infty}A_nw^n$ for $|w|<1/4$. The logarithmic inverse coefficients $Gamma_n$ of $F$ are defined by the formula $logleft(F(w)/wright),=,2sum_{n=1}^{infty}Gamma_n(F)w^n$. % In this paper, we determine the logarithmic inverse coefficients bound of $F$ for the class In this paper, we first determine the sharp bound for the absolute value of $Gamma_n(F)$ when $f$ belongs to $es$ and for all $n geq 1$. This result motivates us to carry forward similar problems for some of its important geometric subclasses. In some cases, we have managed to solve this question completely but in some other cases it is difficult to handle for $ngeq 4$. For example, in the case of convex functions $f$, we show that the logarithmic inverse coefficients $Gamma_n(F)$ of $F$ satisfy the inequality [ |Gamma_n(F)|,le , frac{1}{2n} mbox{ for } ngeq 1,2,3 ] and the estimates are sharp for the function $l(z)=z/(1-z)$. Although this cannot be true for $nge 10$, it is not clear whether this inequality could still be true for $4leq nleq 9$.
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