In this paper, two new subclasses of holomorphic and bi-univalent functions are introduced by using Balancing polynomials. Then, coefficient estmations determined for the first coefficients belonging to these classses. Finally, Fekete-Szeg¨o problem is handled in defined.

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

We consider a compact CR manifold with transversal locally free circle action endowed an S1-equivariant positive line bundle. prove that certain weighted Fourier–Szeg? kernel of the sections in high tensor powers admits full asymptotic expansion. As consequence, we establish equivariant Kodaira embedding theorem.

The minimizers of the anisotropic fractional isoperimetric inequality with respect to a convex body $ K in \mathbb{R}^n are shown be equivalent star bodies whenever is strictly and unconditional. From this Pólya-Szeg? principle for seminorms derived by using symmetrization bodies.

The frequency analysis problem is to determine the unknown frequencies of a trigonometric signal with a sample of size N . Recently there has been established a method for determining those frequencies by using the asymptotic behaviour of the zeros of certain Szeg o polynomials. The Szeg o polynomials in question are orthogonal on the unit circle with respect to an inner product de ned by a m...

Let p be a trigonometric polynomial, nonnegative on the unit circle T. We say that a measure σ on T belongs to the polynomial Szeg˝ o class, if dσ(e iθ) = σ ′ ac (e iθ) dθ + dσ s (e iθ), σ s is singular, and 2π 0 p(e iθ) log σ ′ ac (e iθ) dθ > −∞ For the associated orthogonal polynomials {ϕ n }, we obtain pointwise asymp-totics inside the unit disc D. Then we show that this asymptotics holds in...

We consider the problem of approximating a convex gure in the plane by a pair r R of homothetic that is similar and parallel rectangles with r C R We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle thereby solving a problem posed by P olya and Szeg o If the n vertices of a convex polygon C are given as a sort...

By making use of $q$-derivative and $q$-integral operators, we define a class analytic bi-univalent functions in the unit disk $|z|<1$. Subsequently, investigate some properties such as early coefficient estimates then obtain Fekete-Szeg\"o inequality for both real complex parameters. Further, interesting corollaries are discussed.