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Register a new userInitial estimates for certain subclasses of bi-univalent functions with $kappa-$Fibonacci numbers
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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.
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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.
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 second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting 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.
Inspired by the recent works of Srivastava et al. (HMS-AKM-PG), Frasin and Aouf (BAF-MKA) and others (Ali-Ravi-Ma-Mina-class,Caglar-Orhan,Goyal-Goswami,Xu-HMS-AML,Xu-HMS-AMC), we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions. Also, we obtain estimates on the coefficients |a2| and |a3| for functions in this new class. Some interesting remarks, corollaries and applications of the results presented here are also discussed.
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