A new inequality for a polynomial.
A simple proof of Cauchy theorem
A sufficient condition for starlikeness of analytic functions of Koebe type.
Algebras of holomorphic functions with Hadamard multiplication
A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.
An operator preserving inequalities between polynomials.
Analytic solutions of -th order differential equations at a singular point.
Beweis des Satzes, dass eine eindeutige analytische Function in unendlicher Nähe einer wesentlich singulären Stelle jedem Werth beliebig nahe kommt
Beweis für einen Chauchy'schen Satz
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.
Commutants of the Pommiez operator.
Conditions of analyticity for functions of one complex variable.
Courbes de Jordan vérifiant une condition corde-arc
Soit une courbe de Jordan fermée rectifiable dans le plan de la variable complexe. On dit que véfifie la condition corde-arc sioù est la longueur du plus petit arc de joignant et . Soit une représentation conforme du disque unité dans l’intérieur de . Nous prouvons que restreint à appartient à la classe de Muckenhoupt et nous en tirons certains corollaires. Dans deux cas particuliers nous montrons que le résultat peut être amélioré.
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...
Démonstration nouvelle d'un théorème fondamental sur les suites de fonctions monogènes
Eine komplexe Ungleichung aus elementarer Sicht.
Elementární důkaz Cauchyovy věty pro jednoduše souvislé oblasti