Current Topics In Analytic Function TheoryThis 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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Since CO HRH =s+X B.0)*, (2.2) k=2 we may write (1.2) as D^f(z) = z ¡VXD BECA)ay 2¢X. (2.3) k=2 But, in view of the definition of TA(o), we have fe TA(o) + D*fe T"(a), (2.4) and so Lemma 1 follows immediately from Theorem A. Corollary 1 ...
Since CO HRH =s+X B.0)*, (2.2) k=2 we may write (1.2) as D^f(z) = z ¡VXD BECA)ay 2¢X. (2.3) k=2 But, in view of the definition of TA(o), we have fe TA(o) + D*fe T"(a), (2.4) and so Lemma 1 follows immediately from Theorem A. Corollary 1 ...
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Corollary 3. A function f defined by (1.6) is in R[o., 3), (0 < 0 < 1, 0 < 0 < 1) if and only if 1 ¡V 3 where C(a, k) = II: 20 ¡V 20)/(k-1)!. yo (8¡V3)C(a,b), S 1 , k = 2 Proof. Replace X by 1 ¡V 20 and change o to 3 in Lemma 1, ...
Corollary 3. A function f defined by (1.6) is in R[o., 3), (0 < 0 < 1, 0 < 0 < 1) if and only if 1 ¡V 3 where C(a, k) = II: 20 ¡V 20)/(k-1)!. yo (8¡V3)C(a,b), S 1 , k = 2 Proof. Replace X by 1 ¡V 20 and change o to 3 in Lemma 1, ...
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If 0 < by s 1, then the above observation yields the inequality (2.14) which, on using Lemma 1, proves that f * g e TA(o). This completes the proof of Theorem 2. Corollary. Let f and g be as defined in Theorem 2. If f is in T" (o), ...
If 0 < by s 1, then the above observation yields the inequality (2.14) which, on using Lemma 1, proves that f * g e TA(o). This completes the proof of Theorem 2. Corollary. Let f and g be as defined in Theorem 2. If f is in T" (o), ...
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Corollaries of Theorem 3. Each of the following assertions hold: 1. f,g e T" (o), 0 < a. 3 1 => he T"((40 ¡V 30¢X)/(2 ¡V o¡¨)); f,g e C(o), 0 < o 1 => he T" (203 ¡V 20)/(o¡¨ ¡V 60 + 7)); 2 3. f,g £á R[o], 0 < 0 < 1/2 = net (#4). 4. f,g e Rso, ...
Corollaries of Theorem 3. Each of the following assertions hold: 1. f,g e T" (o), 0 < a. 3 1 => he T"((40 ¡V 30¢X)/(2 ¡V o¡¨)); f,g e C(o), 0 < o 1 => he T" (203 ¡V 20)/(o¡¨ ¡V 60 + 7)); 2 3. f,g £á R[o], 0 < 0 < 1/2 = net (#4). 4. f,g e Rso, ...
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This completes the proof of Theorem 4. The result is sharp for the functions 1 ¡X of 2 sG)=06)==-a-six; Corollaries of Theorem 4. We have the following assertions: 1. f e C(o) => f e T" (2/(3 ¡V oy); 2.
This completes the proof of Theorem 4. The result is sharp for the functions 1 ¡X of 2 sG)=06)==-a-six; Corollaries of Theorem 4. We have the following assertions: 1. f e C(o) => f e T" (2/(3 ¡V oy); 2.
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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
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| ®Ñ¦W | Current Topics In Analytic Function Theory |
| ½sªÌ | Shigeyoshi Owa, Hari M Srivastava |
| ¥Xª©ªÌ | World Scientific, 1992 |
| ISBN | 9814505692, 9789814505697 |
| ¶¼Æ | 472 ¶ |
| ¶×¥X®Ñ¥Ø¸ê®Æ | BiBTeX EndNote RefMan |