Prescribing geometric structures of a complex manifold often introduces interesting and important partial differential equations. A typical example of this kind is the problem of finding the Kähler metrics with constant scalar curvature on a Kähler manifold. Such a problem defines a fourth order elliptic partial differential equation. The study of these partial differential equations, including...

In this work, we obtain the Fekete-Szegö inequalities for the class $P_{Sigma }left( lambda ,phi right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].

A new class of orthogonal polynomials is introduced which generalizes the Bernstein-Szegö polynomials and includes the associated polynomials as well. The purpose of this paper is to give a natural extension of the Bernstein-Szegö orthogonal polynomials for a general class of weight functions. A nonnegative function w defined on the real line is called a weight function if w > 0, fRw > 0 and al...

The results on characterization of orthogonal polynomials and Szegö polynomials via tridiagonal matrices and unitary Hessenberg matrices, resp., are classical. In a recent paper we observed that tridiagonal matrices and unitary Hessenberg matrices both belong to a wide class of (H, 1)–quasiseparable matrices and derived a complete characterization of the latter class via polynomials satisfying ...

The aim of this paper is to gives sharp bound of the Fekete Szegö coefficient functional for the Janowski α-Spirallike functions associated with the kth root transformation. Mathematics Subject Classification: Primary 30C45, Secondary 30C50

In the present investigation we solve Fekete–Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.

In the present work, we aim to introduce and investigate a novel comprehensive subclass of normalized analytic bi-univalent functions involving Gegenbauer polynomials zero-truncated Poisson distribution. For in aforementioned class, find upper estimates second third Taylor–Maclaurin coefficients, then solve Fekete–Szegö functional problem. Moreover, by setting values parameters included our mai...