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.

In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (Rahmanzadeh-Cai-White) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common ...

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By virtue Faber polynomial expansions, estimation n?th(n?3) Taylor–Maclaurin coefficients an obtained. Furthermore, bounds value first two such established.

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.

a simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. the approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. the computational results for the scaled variables are presented through graphs. the effect of the important parameters (1) d...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

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 paper, we introduce and investigate an interesting subclass B Σ of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class B Σ we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent work of Brannan and Taha [1]. AMS Mathematics Subject Classif...

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z?C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 Fekete–Szegö inequalities a3??a22 these subclasses.