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.

Fekete’s lemma is a well known combinatorial result on number sequences: we extend it to functions defined on d-tuples of integers. As an application of the new variant, we show that nonsurjective d-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support’s boundary determined by the automaton’s...

Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions ...

We prove sieve-type lower bounds for the Mahler measure of polynomials on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Abstract. In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b, using a linear multiplier differential operator D λ,μf(z). In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

In the present paper we find a new interpretation of Narayana polynomials Nn(x) which are the generating polynomials for the Narayana numbers Nn,k = 1 n C k−1 n C k n where C i j stands for the usual binomial coefficient, i.e. C j = j! i!(j−i)! . They count Dyck paths of length n and with exactly k peaks, see e.g. [13] and they appeared recently in a number of different combinatorial situations...

A variety of results in complex geometry and mathematical physics depend upon the analysis of holomorphic sections of high powers L⊗N of holomorphic line bundles L → M over compact Kähler manifolds ([A][Bis][Bis.V] [Bou.1][Bou.2][B.G][D][Don] [G][G.S][K][Ji] [T] [W]). The principal tools have been Hörmander’s L-estimate on the ∂̄-operator over M [T], the asymptotics of heat kernels kN (t, x, y) ...

We consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this for a large class of subshifts, namely those satisfying Boshernitzan’s condition. This is accomplished by relating the essential support to uniform convergenc...