The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass. Mathematics Subject Classification: 30C45, 30C50

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...

We introduce and investigate an interesting subclass NP(λ,δ)(Σ) (n, β; h) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NP(λ,δ)(Σ) (n, β; h), we obtain estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃|.

In this article, we establish the bounds for initial Taylor–Maclaurin coefficients |a2| and |a3| a new family G?(?,?,?;h) of holormorphic bi-univalent functions which involve prestarlike functions. Furthermore, investigate Fekete–Szegö type inequality, special cases consequences.

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, find estimates on first two Taylor-Maclaurin coefficients a2 a3 for in these obtain Fekete-Szegö problem subclasses.

In this paper, we define certain families SE*(?) and CE(?) of holomorphic bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö type inequalities these families.

For a certain subclass of Bazilevic functions, Faber polynomials expansions are used to obtain bi-univalent properties. Estimates on the $n$th Taylor-Maclaurin coefficients functions in this class found. Moreover, some special cases also indicated.