We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for functions these Σ are investigated. Using estimates a2,a3, we also discuss Fekete-Szegö inequality results classes this paper. Relevant connections results, presented here as corollaries, not studied...

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...

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...

where the coefficients are Legendre symbols, is called the p-th Fekete polynomial. In this paper the size of the Fekete polynomials on subarcs is studied. We prove essentially sharp bounds for the average value of |fp(z)| , 0 < q < ∞, on subarcs of the unit circle even in the cases when the subarc is rather small. Our upper bounds are matching with the lower bounds proved in a preceding paper f...

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...

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional |a p2 − μa 2 p1 | related to the Fekete-Szegö problem are given.

For non-zero complex b, let N b m,n(φ) (m > n), m ∈ N, n ∈ N0 denote the class of normalized univalent functions f satisfying 1+ 1 b ( Df(z) Dnf(z) − 1 ) ≺ φ(z), z in the open unit disk U , where Dnf denotes the Sălăgean derivative of f . In this paper, we obtain sharp bounds for the Fekete-Szegö functional |a3 − μa2|.