James A. Jenkins

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1. In addition to the study devoted to the general class of normalized regular univalent functions in the unit circle considerable attention has been given to certain subclasses of these functions such as starlike functions, convex functions, and others. In view of the important role played by symmetrization methods in recent work it seems worth while to(More)
1. In a recent paper [2] Reich has made the observation that an example of Koebe given in 1918 [l] does not fulfill its asserted purpose. This example was to show that vanishing measure of the complement did not assure that a slit domain was minimal. Reich proceeded to fill the gap by carrying out the following somewhat more general construction. Let A be a(More)
form expressions for the polynomials for the triangle, for example, are believed not to have been known previously. Certain properties of the polynomials of an orthogonal system for which expressions in closed form exist can be derived easily. This, in fact, motivates the search for them. For instance, for all the systems obtained above the generating(More)
We study the boundary correspondence under sense-preserving homeomorphic self-mapping of the upper half-plane. Under assumptions that involve integrals of the complex dilatation we prove that the natural extension of the mapping is conformal at every point on the boundary. If the integrals involving the complex dilatation are locally uniformly convergent we(More)
Let F„ denote the wth coefficient region for this class of functions [S, §1.2]. Let F=Fia2, ä2, ■ • ■ , a„, a«) be a real-valued function. Write x,= (l/2)(a,+á,), y,= (l/2í)(a,-á,), F,= (l/2)(r3F/r)x, — idF/dy,). Let F satisfy the further conditions (a) F is defined in an open set O containing V„, (b) F and its derivatives F, are continuous in 0, (c) |grad(More)
PURPOSE OF THE REVIEW This review summarizes advances in treatments for adults with borderline personality disorder (BPD) in the last 5 years. RECENT FINDINGS Evidence-based advances in the treatment of BPD include a delineation of generalist models of care in contrast to specialist treatments, identification of essential effective elements of dialectical(More)
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