A new inequality for a polynomial.
A sufficient condition for starlikeness of analytic functions of Koebe type.
An operator preserving inequalities between polynomials.
Bilateral isoperimetric inequalities for boundary moments of plane domains.
Bounds for Vandermonde type determinants of orthogonal polynomials.
Certain sufficient conditions for strongly starlike functions associated with an integral operator.
Co-convexial reflector curves with applications.
Coefficient inequalities for certain classes of analytic and univalent functions.
Criteria for univalence, starlikeness and convexity
Let 𝓐 denote the class of all normalized analytic functions f (f(0) = 0 = f'(0)-1) in the open unit disc Δ. For 0 < λ ≤ 1, define 𝓤(λ) = {f ∈ 𝓐 : |(z/f(z))²f'(z) - 1| < λ, z ∈ Δ} and 𝓟(2λ) = f ∈ 𝓐 : |(z/f(z))''| < 2λ, z ∈ Δ.cr Recently, the problem of finding the starlikeness of these classes has been considered by Obradović and Ponnusamy, and later by Obradović et al. In this paper, the authors consider the problem of finding the order...
Eine komplexe Ungleichung aus elementarer Sicht.
Extensions of Hiong's inequality.
Extremal metrics and modulus
We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in space. Also, some generalizations of Gehring’s result are presented.
Finite-infinite-range inequalities in the complex plane.
Generalized Newton-like inequalities.
Growth of polynomials whose zeros are outside a circle
If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.
Growth of the product
We estimate the maximum of on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when is or when is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when is j. In contrast we show, under fairly general conditions, that the maximum is less than , where r is an arbitrary positive number. One consequence is that the...
Hardy type inequalities in higher dimensions with explicit estimate of constants.
Holomorphic Lipschitz functions in balls.
Inclusion and neighborhood properties for certain classes of multivalently analytic functions associated with the convolution structure.
Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions
MSC 2010: 33E12, 30A10, 30D15, 30E15We consider some families of 3-index generalizations of the classical Mittag-Le²er functions and study the behaviour of these functions in domains of the complex plane. First, some inequalities in the complex plane and on its compact subsets are obtained. We also prove an asymptotic formula for the case of "large" values of the indices of these functions. Similar results have also been obtained by the author for the classical Bessel functions and their Wright's...