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 26 頁
... Corollary 1. The extreme points of CA, -1 < X • 1, are the functions given by - (1 + X) - G1(z) = 2, GoG)=== III. H.H.O.W.' (k = 2, 3,...). Corollary 2. The extreme points of Rso, 3], a « 1 and 0 < 3 < 1, are the functions given by 1 ...
... Corollary 1. The extreme points of CA, -1 < X • 1, are the functions given by - (1 + X) - G1(z) = 2, GoG)=== III. H.H.O.W.' (k = 2, 3,...). Corollary 2. The extreme points of Rso, 3], a « 1 and 0 < 3 < 1, are the functions given by 1 ...
第 27 頁
... Corollary 3 yields the distortion theorem, obtained in [12], for the class K[a]. Corollary 4. With the conditions stated in Corollary 3, the unit disk A is mapped under any function f £ T\{a)onto a domain that contains the disk l + A(2 ...
... Corollary 3 yields the distortion theorem, obtained in [12], for the class K[a]. Corollary 4. With the conditions stated in Corollary 3, the unit disk A is mapped under any function f £ T\{a)onto a domain that contains the disk l + A(2 ...
第 32 頁
... substitution. For w > 2, y + 2w is larger than y” + wy” – 3y – 2w, and the result follows for this case as well. The case w = 0 and the sharpness are immediate. As an immediate consequence of Lemma 1, we have Corollary 32.
... substitution. For w > 2, y + 2w is larger than y” + wy” – 3y – 2w, and the result follows for this case as well. The case w = 0 and the sharpness are immediate. As an immediate consequence of Lemma 1, we have Corollary 32.
第 33 頁
... Corollary 1. Let y > −1 and r(z) = 1 + y2 + raz” + ... be in PR. Then r2 < 2 and r3 s 2 + y. The result is sharp. 3. The Constraint Coefficient Problem in Sr. and CR The immediate application of Lemma 1 is Theorem 1. Let g(z) = z + cz ...
... Corollary 1. Let y > −1 and r(z) = 1 + y2 + raz” + ... be in PR. Then r2 < 2 and r3 s 2 + y. The result is sharp. 3. The Constraint Coefficient Problem in Sr. and CR The immediate application of Lemma 1 is Theorem 1. Let g(z) = z + cz ...
第 44 頁
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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