A Strong Maximum Modulus Theorem For Maximal Function Algebras

1959 ◽  
Vol 92 (3) ◽  
pp. 465 ◽  
Author(s):  
H. S. Bear
Keyword(s):  
Maximal Function ◽  
Maximum Modulus ◽  
Function Algebras ◽  
Maximum Modulus Theorem

scholarly journals Some Inequalities for the Maximum Modulus of Rational Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Robert Gardner ◽  
Narendra Kumar Govil ◽  
Prasanna Kumar
Keyword(s):  
Maximum Modulus ◽  
Rational Functions ◽  
Maximum Modulus Theorem

For a polynomial p z of degree n , it follows from the maximum modulus theorem that max z = R ≥ 1 p z ≤ R n max z = 1 p z . It was shown by Ankeny and Rivlin that if p z ≠ 0 for z < 1 , then max z = R ≥ 1 p z ≤ R n + 1 / 2 max z = 1 p z . In 1998, Govil and Mohapatra extended the above two inequalities to rational functions, and in this paper, we study the refinements of these results of Govil and Mohapatra.

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