Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions

AMS Subj. Classification: 30C4

Koebe domain of starlike functions of complex order with Montel normalization

Let S*(1-b), (b 0 complex) denote the class of functions f(z) = z + a2z2 + ... analytic in D = {z : |z| < 1} which satisfies for z = eiθ D, f(z) / z 0 in D, and Re[1 + 1/b(z f\u27(z) / f(z) - 1)] > 0. The aim of this paper is to give the Koebe domain of the above mentioned class

Koebe domain of starlike functions of complex order with Montel normalization

Let S*(1-b), (b 0 complex) denote the class of functions f(z) = z + a2z2 + ... analytic in D = {z : |z| < 1} which satisfies for z = eiθ D, f(z) / z 0 in D, and Re[1 + 1/b(z f\u27(z) / f(z) - 1)] > 0. The aim of this paper is to give the Koebe domain of the above mentioned class

On quasiconformal harmonic mappings lifting to minimal surfaces

We prove a growth theorem for a function to belong to the class Sigma(mu; a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L-3. We also obtain some estimates of the Gaussian curvature of. the minimal surfaces in 3-dimensional Euclidean space R-3 and of the spacelike minimal surfaces in L-3

Reciprocal classes of <it>p</it>-valently spirallike and <it>p</it>-valently Robertson functions

<p>Abstract</p> <p>For <it>p</it>-valently spirallike and <it>p</it>-valently Robertson functions in the open unit disk <inline-formula><m:math name="1029-242X-2011-61-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>U</m:mi> </m:math> </inline-formula>, reciprocal classes <inline-formula><m:math name="1029-242X-2011-61-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow> <m:msub> <m:mrow> <m:mi mathvariant="script">S</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>&#945;</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>&#946;</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mrow> </m:math> </inline-formula>, and <inline-formula><m:math name="1029-242X-2011-61-i3" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub> <m:mrow> <m:mi mathvariant="script">C</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>&#945;</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>&#946;</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:math> </inline-formula> are introduced. The object of the present paper is to discuss some interesting properties for functions <it>f</it>(<it>z</it>) belonging to the classes <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1029-242X-2011-61-i2"><m:mrow> <m:msub><m:mrow><m:mi mathvariant="script">S</m:mi></m:mrow><m:mrow><m:mi>p</m:mi></m:mrow></m:msub><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>&#945;</m:mi><m:mo class="MathClass-punc">,</m:mo><m:mi>&#946;</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow> </m:mrow></m:math> </inline-formula> and <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1029-242X-2011-61-i3"><m:msub><m:mrow><m:mi mathvariant="script">C</m:mi></m:mrow><m:mrow><m:mi>p</m:mi></m:mrow></m:msub><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>&#945;</m:mi><m:mo class="MathClass-punc">,</m:mo><m:mi>&#946;</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math> </inline-formula>.</p> <p><b>2010 Mathematics Subject Classification</b></p> <p>Primary 30C45</p

Koebe domain of starlike functions of complex order with Montel normalization

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal