Current Topics In Analytic Function TheoryShigeyoshi Owa, Hari M Srivastava World Scientific, 1992年12月31日 - 472 頁 This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju. |
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第 1 到 5 筆結果,共 84 筆
第 4 頁
... Lemma 1 follows. An analogous result holds also for ring domains. Lemma 2. Let f be a nonvanishing continuous function defined on the boundary dA(r,l) of the annulus A(r,l). Then there exists for each /3, Re /3 > —1/2,a unique mapping f ...
... Lemma 1 follows. An analogous result holds also for ring domains. Lemma 2. Let f be a nonvanishing continuous function defined on the boundary dA(r,l) of the annulus A(r,l). Then there exists for each /3, Re /3 > —1/2,a unique mapping f ...
第 5 頁
... Lemma 1, the functions h and g depend on the values of 0. The next Lemma will be used later on. It refers to the dilatation function a{z) defined in (2). Lemma 3. Let f(z) = z\z\2f3hg~ be a logharmonic mapping defined on a domain D ...
... Lemma 1, the functions h and g depend on the values of 0. The next Lemma will be used later on. It refers to the dilatation function a{z) defined in (2). Lemma 3. Let f(z) = z\z\2f3hg~ be a logharmonic mapping defined on a domain D ...
第 6 頁
... the argument principle, f is univalent on D, for all t e [0, 2T). Hence, f is univalent on D. Finally, suppose that f(A(r. 1) # Q. Since, by Lemma 4, Q is contained in f(A(r. 1)) we conclude that f is not an open mapping, i.e., there.
... the argument principle, f is univalent on D, for all t e [0, 2T). Hence, f is univalent on D. Finally, suppose that f(A(r. 1) # Q. Since, by Lemma 4, Q is contained in f(A(r. 1)) we conclude that f is not an open mapping, i.e., there.
第 7 頁
... (Lemma 3) and this case is excluded. 3. Logharmonic Disk Mappings In this section we consider the logharmonic solution of the Dirichlet problem of the unit disk. Let f(z) = z|z|*hy be a logharmonic mapping from U onto U and continuous on ...
... (Lemma 3) and this case is excluded. 3. Logharmonic Disk Mappings In this section we consider the logharmonic solution of the Dirichlet problem of the unit disk. Let f(z) = z|z|*hy be a logharmonic mapping from U onto U and continuous on ...
第 17 頁
... Lemma 1 follows immediately from Theorem A. Corollary 1. Let f be of the form (1.6), X > −1 and 0 < o 3 1. If fe TA(o), then 1 — a < — * = (ETC)B.O) with equality for functions of the form (k > 2), 1 — a k Fe(s)====ED)". Corollary 2. A ...
... Lemma 1 follows immediately from Theorem A. Corollary 1. Let f be of the form (1.6), X > −1 and 0 < o 3 1. If fe TA(o), then 1 — a < — * = (ETC)B.O) with equality for functions of the form (k > 2), 1 — a k Fe(s)====ED)". Corollary 2. A ...
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Amer analytic functions Bergman spaces bounded class of functions close-to-convex completes the proof complex plane convex functions convex sets Corollary defined denote the class Department of Mathematics derivative differential equation domains of univalence entire function euclidean extremal functions Fatou set Fractional Calculus function f(z functions with negative given H. M. Srivastava half-plane Hence holomorphic functions hyperbolic hypergeometric functions implies integral operator Julia set Lemma Little Picard Theorem locally schlicht logharmonic mapping Math meromorphic functions normal Nunokawa obtain p-valently starlike P. T. Mocanu problem Proc proof of Theorem properties radius Re(z real number Remark Rep(z result is sharp Ruscheweyh Saigo sharp for functions spherical linear invariance spherically convex starlike and convex starlike functions strictly increasing subclass Suppose TA(o unit disk Univ univalence for F(K univalent functions zero divisor zero set