Current Topics In Analytic Function TheoryShigeyoshi Owa, Hari M Srivastava World Scientific, 1992¦~12¤ë31¤é - 472 ¶ 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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... problem w.r.to f". Then f is univalent on D and f(D) = Q if and only if |a| < 1 on U. Proof. (a) Suppose first that D = U and that Q is simply-connected. Let f be univalent on U. Then |a|{2) # 1 for all 2 £á U. Hence, either |a| > 1 or ...
... problem w.r.to f". Then f is univalent on D and f(D) = Q if and only if |a| < 1 on U. Proof. (a) Suppose first that D = U and that Q is simply-connected. Let f be univalent on U. Then |a|{2) # 1 for all 2 £á U. Hence, either |a| > 1 or ...
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... problem of the unit disk. Let f(z) = z|z|*hy be a logharmonic mapping from U onto U and continuous on U. Then f(e") = e¡¨h(e¡¨)g(e") is well defined and we have |f(e¡¨)| = |h(e").g(e") = 1. Since h and g are analytic and nonvanishing, we ...
... problem of the unit disk. Let f(z) = z|z|*hy be a logharmonic mapping from U onto U and continuous on U. Then f(e") = e¡¨h(e¡¨)g(e") is well defined and we have |f(e¡¨)| = |h(e").g(e") = 1. Since h and g are analytic and nonvanishing, we ...
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... problem where Re /9 > ¡X1/2 and 21og h is defined by (6). Then f is a univalent mapping from U onto U such that the unrestricted limits lim^ „.« f(z) = /*(e**) exist on dU\E, where E is a countable set. 4. Logharmonic Ring Mappings Let ...
... problem where Re /9 > ¡X1/2 and 21og h is defined by (6). Then f is a univalent mapping from U onto U such that the unrestricted limits lim^ „.« f(z) = /*(e**) exist on dU\E, where E is a countable set. 4. Logharmonic Ring Mappings Let ...
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... problem with respect to f" and A(r. 1) is a univalent mapping from A(r. 1) onto A(R, 1). Proof. We will show that the relations (i) to (iv) and (9) in Theorem C hold. By hypothesis, f is of the form (3) with Re 6 ¡Ñ −1/2 and h and g are ...
... problem with respect to f" and A(r. 1) is a univalent mapping from A(r. 1) onto A(R, 1). Proof. We will show that the relations (i) to (iv) and (9) in Theorem C hold. By hypothesis, f is of the form (3) with Re 6 ¡Ñ −1/2 and h and g are ...
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... problem with respect to /„* denned by /„*(ei() = eiA"W and fn*(reu) = Reilin^ satisfy Re (1 + ^r-"-) > 0 on A(r, 1) and they converge locally uniformly to / on A(r, 1). Therefore, (i) holds for / and Theorem 4 is established. References ...
... problem with respect to /„* denned by /„*(ei() = eiA"W and fn*(reu) = Reilin^ satisfy Re (1 + ^r-"-) > 0 on A(r, 1) and they converge locally uniformly to / on A(r, 1). Therefore, (i) holds for / and Theorem 4 is established. References ...
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