Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (5): 1929-1936.doi: 10.1016/S0252-9602(12)60150-7

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THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES

 PENG Zhi-Gang   

  1. Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China
  • Received:2011-02-18 Online:2012-09-20 Published:2012-09-20
  • Supported by:

    Supported by Educational Commission of Hubei Province of China (D2011006).

Abstract:

Let ζ = (0, z1, z2, · · · , zn) with |zj| < 1 for 1 ≤ j ≤ n, ! = (1, w1, w2, · · · , wn), and P(ζ, ω) denote the set of functions p(z) that are analytic in D = {z : |z| < 1} and satisfy Rep(z) > 0 (|z| < 1), p(0) = 1, p(zj) = wj , j = 1, 2, · · · , n. In this article we investigate the extreme points of P(ζ, ω).

Key words: extreme point, positive real part, Blaschke product

CLC Number: 

  • 30C45
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