Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson Borel Mittag-Leffler-type Miller–Ross-Type Distribution. In present paper, making use Bell we introduce investigate a new family GΣt(x,p,q,λ,β,γ) normalized functions in open unit disk U, which are associated with Horadam polyn...

Giving a (partial) solution to a problem of S. Fekete [3] and S. Fekete and G.J. Woeginger [4] we show that given a finite set X of points in the plane, it is possible to find a polygonal path with |X|−1 segments and with vertex set X so that every angle on the polygonal path is at least π/9. According to a conjecture of Fekete and Woeginger, π/9 can be replaced by π/6. Previously, the result h...

The present study’s intention is to produce exact estimations of some problems involving logarithmic coefficients for functions belonging the considered subcollection B mathvariant="script">T mathvariant="normal">sin bounded turning class. Furthermore, class id...

In this communication we present a new method to estimate Fekete points on surfaces. Our method works in a general setting, in the sense that we can obtain good estimations of the Fekete points on piecewise regular surfaces. The determination of Fekete points in the unit sphere is considered as a model of a highly non-linear optimization problem with non-linear constraints. In fact, obtaining a...

We present here strong numerical and statistical evidence of the fact that the Smale’s 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the 2-sphere satisfying the Smale’s conditions can be identified with a computational cost of approximately O(N10).

The objective of this work is to provide a methodology for approximating globally optimal Fekete point con-gurations. This problem is of obvious interest in numerical mathematics and scientic modeling. Following a brief discussion of the pertinent analytical background, Lipschitz global optimization (LGO) is applied to determine {i.e., to numerically approximate{ Fekete point congurations. Next...

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.