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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 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 Feket
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
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 concerni
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 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.