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Zeros of solutions of certain higher order linear differential equations

Hong-Yan XuCai-Feng Yi — 2010

Annales Polonici Mathematici

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + + a ( z ) f ' + D ( z ) f = 0 , (1) where D ( z ) = Q ( z ) e P ( z ) + Q ( z ) e P ( z ) + Q ( z ) e P ( z ) , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), a j ( z ) (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

An improvement of Hayman's inequality on an angular domain

Cai-Feng YiYu WangHong-Yan Xu — 2010

Annales Polonici Mathematici

We investigate the properties of meromorphic functions on an angular domain, and obtain a form of Yang's inequality on an angular domain by reducing the coefficients of Hayman's inequality. Moreover, we also study Hayman's inequality in different forms, and obtain accurate estimates of sums of deficiencies.

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