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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第 1 到 5 筆結果，共 91 筆
第 4 頁
In other words, we are looking Tor a continuous mapping in U which is of the form f(z) = z\z\2/1hg; Re fi > —1/2, h,g G H(U) and nonvanishing, g(0) = 1 such that / is equal to a given continuous boundary function f on dU. Lemma 1.
In other words, we are looking Tor a continuous mapping in U which is of the form f(z) = z\z\2/1hg; Re fi > —1/2, h,g G H(U) and nonvanishing, g(0) = 1 such that / is equal to a given continuous boundary function f on dU. Lemma 1.
第 7 頁
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 ... Since h and g are analytic and nonvanishing, we conclude that f(z) = e^2|z|*h(z)/h(z), Re 6 - –1/2.
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 ... Since h and g are analytic and nonvanishing, we conclude that f(z) = e^2|z|*h(z)/h(z), Re 6 - –1/2.
第 8 頁
Differentiation with respect to z gives 2h' 1 r2ir 9p-«* Jo (1-e-*s)21wJ' h 2TM and integration by parts leads to 9/i' 1 /-2ir 1 /i Wo z(l- e-'z) L W J and 2/)' 1 r>f 1 1 + 2^- = 1 + 2 - / -—L_d[ A {<)_fl. re 27T Vo 1 — e " 2 Since /02 ...
Differentiation with respect to z gives 2h' 1 r2ir 9p-«* Jo (1-e-*s)21wJ' h 2TM and integration by parts leads to 9/i' 1 /-2ir 1 /i Wo z(l- e-'z) L W J and 2/)' 1 r>f 1 1 + 2^- = 1 + 2 - / -—L_d[ A {<)_fl. re 27T Vo 1 — e " 2 Since /02 ...
第 10 頁
Observe that (iii) implies Re 6 » -1/2 and that Re 6 depends only on r and R. Our main result of this section is ... Since |h.g| = 1 on 6U and |h.g| = R/r” on the circle {z;|z|= r) it follows that hg = e^z" for some m e 2 and some a e ...
Observe that (iii) implies Re 6 » -1/2 and that Re 6 depends only on r and R. Our main result of this section is ... Since |h.g| = 1 on 6U and |h.g| = R/r” on the circle {z;|z|= r) it follows that hg = e^z" for some m e 2 and some a e ...
第 11 頁
If A and /J. are continuously differentiable on [0,2w), then the harmonic function Re |£(/>e*() is not identically zero and we have, for z = peH, Re%(peil) = Re (1+~) > 0. If A and fi are arbitrary nondecreasing functions of total ...
If A and /J. are continuously differentiable on [0,2w), then the harmonic function Re |£(/>e*() is not identically zero and we have, for z = peH, Re%(peil) = Re (1+~) > 0. If A and fi are arbitrary nondecreasing functions of total ...
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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
書目資訊
| 書名 | Current Topics In Analytic Function Theory |
| 編者 | Shigeyoshi Owa, Hari M Srivastava |
| 出版者 | World Scientific, 1992 |
| ISBN | 9814505692, 9789814505697 |
| 頁數 | 472 頁 |
| 匯出書目資料 | BiBTeX EndNote RefMan |