منابع مشابه
A Relative of the Lemma of Schwarz*
so that d(r, 0; ƒ') is the length of the segment on the w-plane between the image of the point 3 = 0 and the image of the point z = re. The lemma of Schwarz is the following: THEOREM 1. Let w=f(z) be analytic f or \z\ < 1 . If d(r,6;f)S 1 for all (r, 6) with r<l, then (1) d(r,0;f)gr and (2) | / ( 0 ) | ^ 1 . The sign of equality holds in (1) (for r^O) and in (2), if and only if \f(z) | = 1 ; th...
متن کاملConstrained versions of Sauer's lemma
Let [n] = {1, . . . , n}. For a function h : [n] → {0, 1}, x ∈ [n] and y ∈ {0, 1} define by the width ωh(x, y) of h at x the largest non-negative integer a such that h(z) = y on x− a ≤ z ≤ x+ a. We consider finite VC-dimension classes of functions h constrained to have a width ωh(xi, yi) which is larger than N for all points in a sample ζ = {(xi, yi)}1 or a width no larger than N over the whole...
متن کاملSome Applications of Schwarz Lemma for Operators
A generalized Schwarz lemma and some Harnack type inequalities for operators have been obtained in this paper.
متن کاملA Schwarz Lemma for Correspondences and Applications
A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the ‘non-increasing’ property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a ‘non-compact’ family of proper correspon-
متن کاملJulius and Julia: Mastering the Art of the Schwarz Lemma
This article discusses classical versions of the Schwarz lemma at the boundary of the unit disk in the complex plane. The exposition includes commentary on the history, the mathematics, and the applications.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1997
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5217