Convex and alpha-prestarlike subordination chains

Subordination Properties for Certain Subclasses of Prestarlike Functions

Making use of generalized Sǎlǎgean derivative operator in this paper, we define a unified class of starlike functions with negative coefficients and obtain subordination results, partial sums, integral transforms for this class. Further integral means and square root transformation results are discussed. AMS (MOS) Subject Classification Codes: 30C45

Subordination by convex functions

Subordination by Convex Functions

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...

Energy characteristics of subordination chains

We consider subordination chains of simply connected domains with smooth boundaries in the complex plane. Such chains admit Hamiltonian and Lagrangian interpretations through the Löwner-Kufarev evolution equations. The action functional is constructed and its time variation is obtained. It represents the infinitesimal version of the action of the Virasoro-Bott group over the space of analytic u...

On the convolution and subordination of convex functions

In this work we present some new results on convolution and subordination in geometric function theory. We prove that the class of convex functions of order α is closed under convolution with a prestarlike function of the same order. Using this, we prove that subordination under the convex function order α is preserved under convolution with a prestarlike function of the same order. Moreover, w...