In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing ideas subordination Sălăgean quantum differential operator. The primary contribution article is derivation sharp inequality for newly established subclasses in open unit disc U. For novel family, bounds first two Taylor–Maclaurin coefficients, Fekete–Szegö-type functional, coeffic...

We recall some results from a paper by Szego on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the e...

It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either...

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

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 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].

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...