Coefficient estimates for exponential series

Coefficient Estimates for Univalent Functions

Coefficient estimates for Ruscheweyh derivatives

are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

Estimates for “Singular” Exponential Sums

In [D1, Thm. 8.4], Deligne proved the following beautiful estimate for exponential sums in n ≥ 1 variables. Given a polynomial f(x1, . . . , xn) in n variables over k of some degree d ≥ 1, write it as f = Fd + Fd−1 + · · · F0 with Fi homogeneous of degree i. Suppose that the following two conditions are satisfied. (1) The degree d is prime to p := char(k). (2) The locus Fd = 0 is a nonsingular ...

Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

Combined Bayesian Estimates for the Equicorrelation Coefficient

Combined Bayesian estimates for equicorrelation covariance matrices are considered. The case of a common equicorrelation p and possibly different standard eviations I,...,aok among k experimental groups is examined first, and the Bayesian estimation of (p, al,...,(k) is discussed. Secondly, under the assumption of a common standard eviation and possibly different equicorrelations, the Bayesian ...