Journal of the Ramanujan Mathematical Society

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An Application of Borel-Caratheodory Theorem


Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400 005, India
     

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The theorem in the title (see p.174 of [7]) is the following one.

Theorem 1: if f(z') is analytic in |z| ≤ 1 and f(0) = 0 ,

Then

|f(z)| ≤ 2(2A(f)) |z|/1-|z|.........(1)


Keywords

Borel - Caratheodory Theorem, Maximum Modulus Principle.
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  • An Application of Borel-Caratheodory Theorem

Abstract Views: 166  |  PDF Views: 0

Authors

K. Ramachandra
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400 005, India

Abstract


The theorem in the title (see p.174 of [7]) is the following one.

Theorem 1: if f(z') is analytic in |z| ≤ 1 and f(0) = 0 ,

Then

|f(z)| ≤ 2(2A(f)) |z|/1-|z|.........(1)


Keywords


Borel - Caratheodory Theorem, Maximum Modulus Principle.