Region of variability for spiral-like functions with respect to a boundary point

Region of Variability for Spirallike Functions with Respect to a Boundary Point

We denote the class of analytic functions in the unit disk D = {z ∈ C : |z| < 1} by H(D), and we think of H(D) as a topological vector space endowed with the topology of uniform convergence over compact subsets of D. Denote by S∗ the subclass of functions φ ∈ H(D) with φ(0) = 0 such that φ maps D univalently onto a domain Ω = φ(D) that is starlike with respect to the origin. That is, tφ(z) ∈ φ(...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

Angle distortion theorems for starlike and spirallike functions with respect to a boundary point

It is clear that 0∈ h(Δ). Moreover, (i) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to an interior point; (ii) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to a boundary point. In this case, there is a boundary point (say, z = 1) such that h(1) := ∠ limz→1h(z)= 0 (see, e.g., [1, 6]); by symbol∠ lim, we denote the angular (nontangential) lim...

The class of functions spirallike with respect to a boundary point

The aim of this paper is to present an analytic characterization of the class of functions δ-spirallike with respect to a boundary point. The method of proof is based on Julia's lemma.

A Framework for Urban Morphology with Respect to the Form