In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers.  Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.

We present the software package WAM, written in Matlab, that generates Weakly Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d polynomial least squares and interpolation on compact sets with various geometries. Possible applications range from data fitting to high-order methods for PDEs.

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

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.

Let H be the class of functions f(z) of the form f(z) = z + ∑∞ n=2 anz , which are analytic in the unit disk U = {z : |z| < 1}. In this paper, the authors introduce a subclass M (α, λ, ρ) of H and study its some properties. The subordination relationships, inclusion relationships, coefficient estimates, the integral operator and covering theorem are proven here for each of the function classes....

Coefficient bounds for some subclasses of p-valently starlike functions Abstract. For functions of the form f(z) = z+ ∑∞ n=1 ap+nz p+n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete–Szegö-like inequality for classes of functions defined through extended fractiona...

Littlewood asked how small the ratio ||f || 4 /||f || 2 (where ||·|| α denotes the L α norm on the unit circle) can be for polynomials f having all coefficients in {1, −1}, as the degree tends to infinity. Since 1988, the least known asymptotic value of this ratio has been 4 7/6, which was conjectured to be minimum. We disprove this conjecture by showing that there is a sequence of such polynom...

We give lower bounds for the Mahler measure of polynomials with constrained coefficients, including Littlewood polynomials, on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Finding a feasible solution for a bi-dimensional Orthogonal Packing Problem (OPP2) consists in deciding whether a set of rectangular boxes (items) can be packed in a ”big” rectangular container without overlapping. The rotation of items is not allowed. In this paper we present a new algorithm for solving OPP-2, based on the characterization of solutions using interval graphs proposed by Fekete ...

We study the asymptotic equidistribution of points with discrete energy close to Robin’s constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of this equidistribution. Applications include estimates of growth for the Fekete and Leja polynomials associated with large classes of compact sets, convergence r...