Find the value of Given function?











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Let, $f(z)$ be analytics in $|z| le 1$ and $|f(z) |le 1$ with $f(0) = frac{1 +i}{sqrt 2}$ . Then find the value of $f(i) -f(1)$



I Thinks it will be $0$ by Liouville theorem.



Is Its correct ??






complex-analysis







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  • 1




    Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
    – José Carlos Santos
    Nov 19 at 15:14












  • Okkkss sir @jose Carlos santos
    – santosh
    Nov 19 at 15:17















up vote
0
down vote

favorite












Let, $f(z)$ be analytics in $|z| le 1$ and $|f(z) |le 1$ with $f(0) = frac{1 +i}{sqrt 2}$ . Then find the value of $f(i) -f(1)$



I Thinks it will be $0$ by Liouville theorem.



Is Its correct ??






complex-analysis







share|cite|improve this question




















  • 1




    Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
    – José Carlos Santos
    Nov 19 at 15:14












  • Okkkss sir @jose Carlos santos
    – santosh
    Nov 19 at 15:17













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let, $f(z)$ be analytics in $|z| le 1$ and $|f(z) |le 1$ with $f(0) = frac{1 +i}{sqrt 2}$ . Then find the value of $f(i) -f(1)$



I Thinks it will be $0$ by Liouville theorem.



Is Its correct ??






complex-analysis







share|cite|improve this question















Let, $f(z)$ be analytics in $|z| le 1$ and $|f(z) |le 1$ with $f(0) = frac{1 +i}{sqrt 2}$ . Then find the value of $f(i) -f(1)$



I Thinks it will be $0$ by Liouville theorem.



Is Its correct ??






complex-analysis




complex-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 19 at 17:43









Empty

8,04742358




8,04742358










asked Nov 19 at 15:11









santosh

898




898








  • 1




    Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
    – José Carlos Santos
    Nov 19 at 15:14












  • Okkkss sir @jose Carlos santos
    – santosh
    Nov 19 at 15:17














  • 1




    Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
    – José Carlos Santos
    Nov 19 at 15:14












  • Okkkss sir @jose Carlos santos
    – santosh
    Nov 19 at 15:17








1




1




Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
– José Carlos Santos
Nov 19 at 15:14






Since Liouville's theorem is for entire functions, I don't see how you plan to apply it here.
– José Carlos Santos
Nov 19 at 15:14














Okkkss sir @jose Carlos santos
– santosh
Nov 19 at 15:17




Okkkss sir @jose Carlos santos
– santosh
Nov 19 at 15:17










1 Answer
1






active

oldest

votes

















up vote
2
down vote



accepted










Hint : $|f(0)|=1$. Use Maximum Modulus Theorem, which states that "A non constant analytic function in a domain $D$ attains maximum value on it's boundary $partial D$.






share|cite|improve this answer























  • Then answer will be 0 na??
    – santosh
    Nov 19 at 15:17






  • 1




    @santosh Yeah !
    – Empty
    Nov 19 at 15:18











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










Hint : $|f(0)|=1$. Use Maximum Modulus Theorem, which states that "A non constant analytic function in a domain $D$ attains maximum value on it's boundary $partial D$.






share|cite|improve this answer























  • Then answer will be 0 na??
    – santosh
    Nov 19 at 15:17






  • 1




    @santosh Yeah !
    – Empty
    Nov 19 at 15:18















up vote
2
down vote



accepted










Hint : $|f(0)|=1$. Use Maximum Modulus Theorem, which states that "A non constant analytic function in a domain $D$ attains maximum value on it's boundary $partial D$.






share|cite|improve this answer























  • Then answer will be 0 na??
    – santosh
    Nov 19 at 15:17






  • 1




    @santosh Yeah !
    – Empty
    Nov 19 at 15:18













up vote
2
down vote



accepted







up vote
2
down vote



accepted






Hint : $|f(0)|=1$. Use Maximum Modulus Theorem, which states that "A non constant analytic function in a domain $D$ attains maximum value on it's boundary $partial D$.






share|cite|improve this answer














Hint : $|f(0)|=1$. Use Maximum Modulus Theorem, which states that "A non constant analytic function in a domain $D$ attains maximum value on it's boundary $partial D$.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 19 at 15:17

























answered Nov 19 at 15:14









Empty

8,04742358




8,04742358












  • Then answer will be 0 na??
    – santosh
    Nov 19 at 15:17






  • 1




    @santosh Yeah !
    – Empty
    Nov 19 at 15:18


















  • Then answer will be 0 na??
    – santosh
    Nov 19 at 15:17






  • 1




    @santosh Yeah !
    – Empty
    Nov 19 at 15:18
















Then answer will be 0 na??
– santosh
Nov 19 at 15:17




Then answer will be 0 na??
– santosh
Nov 19 at 15:17




1




1




@santosh Yeah !
– Empty
Nov 19 at 15:18




@santosh Yeah !
– Empty
Nov 19 at 15:18


















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