Let denote the normalized, generalized Bessel function of order which depends on two parameters and and let , . It is proven that under some conditions imposed on , , and the Askey inequality holds true for the function , i.e., that , where and . The lower and upper bounds for the function are also established.
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denote the normalized, generalized Bessel function of order 
which depends on two parameters 
and 
and let 
, 
. It is proven that under some conditions imposed on 
, i.e., that 
, where 
and 
. The lower and upper bounds for the function 
