Let be a polynomial of degree at most which does not vanish in the disk , then for and , Boas and Rahman proved In this paper, we improve the above inequality for by involving some of the coefficients of the polynomial . Analogous result for the class of polynomials having no zero in is also given.
A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function is said to be p-harmonic in Ω if each component function (i∈ 1,...,m) of is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings f from...
Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for where is a latent root of a lambda-matrix. In particular, upper bounds for are obtained where is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for .
We present a survey of the Lusin condition (N) for -Sobolev mappings defined in a domain G of . Applications to the boundary behavior of conformal mappings are discussed.
MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in this paper to prove other results, which should not continue.