The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z Ip r, λ f z j 1 / p − j Ip r, λ f z j ≺ a aB A − B β z /a 1 Bz , where Ip r, λ is an operator defined by Sălăgean and β is a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting pr...

We prove the Fekete-Szegö Theorem with splitting conditions for adelic sets on a smooth, connected algebraic curve defined over a number field.

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

A breakthrough paper written in 1993 by Shub and Smale unveiled the relationship between stable polynomials and points which minimize the discrete logarithmic energy on the Riemann sphere (a.k.a. elliptic Fekete points). This relationship has inspired advances in the study of both concepts, many of whose main properties are not well known yet. In this paper I prove an equivalent formulation for...

In this paper we obtain the Fekete-Szegö inequality for a class of analytic functions f(z) defined in the open unit disk for which

Tensor products of Gauss-Lobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if Gauss-Lobatto points exist in non-tensor-product domains like the simplex. In this work, we show that the n-dimensional tensor-product of Gauss-Lobatto quadrature points are also Fekete points. This suggests a way to generalize spectral meth...

In this present investigation, the authors obtain a sharp Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which (1 + β) ( z f(z) )α − βf ′(z) ( z f(z) )1+α , (β ∈ C, 0 < α < 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also, certain applications of our results for a class of functions de...