Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Liang Tang and Ting Zhong
Pages: [39] - [48]
Received Date: July 26, 2014
Submitted by:
Given any infinite set B of positive integers 
let 
For any 
let 
and be the n-th partial quotients
of regular and generalized continued fraction expansion of x,
respectively. Define
Hirst [4] proved the inequality 
for any infinite set B and the
equality 
for 
where 
denotes the Hausdorff dimension. In this
note, we show that 
is twice the size of 
for all the above cases.
regular continued fraction, generalized continued fraction, the sequences of partial quotients, Hausdorff dimension.
