We obtain the Fekete-Szegö inequalities for the classes S S,Σ (*)(α, ϕ) and £ S,Σ(α, ϕ) of biunivalent functions denoted by subordination. The results presented in this paper improve the recent work of Crisan (2013).

In this paper, we introduce and investigate a new subclass of biunivalent functions ∑ of complex order defined in the open unit disk, which are associated with hypergeometric functions and satisfy subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients 2 | | a and 3 | | a for functions in the new subclass. Several (known or new) consequences of the results ar...

In this paper, we introduce and investigate a new subclass of the function class Σ of biunivalent functions of the Bazilevic̆ type defined in the open unit disk, which are associated with the Hohlov operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Several (known...

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass biunivalent functions. We obtained coefficient inequalities for belonging to the subclass. In addition these results, upper bound Fekete-Szegö functional was obtained. Finally, some special values parameters, several corollaries were presented.

In the present paper, a subclass of analytic and biunivalent functions by means Gegenbauer polynomials is introduced. Certain coefficients bound for belonging to this are obtained. Furthermore, Fekete-Szegö problem solved. A number known or new results shown follow upon specializing parameters involved in our main results.