ABSTRACT
By combining all of our results and using Theorem 3.2 i we have proved the following theorem.
As a consequence of this theorem we have the following result.
For our next application we use Corollary 3.2j.l with ~ = 1, "( = 1 and h(z) = (1 + z)/(1 - z). In this case (3.3-2) and ( 3.3-3) become
Kn(Z) - lt;n,t;n[ k ](z) = ( _2_ fz t(Z/n) - 1 dt Jn nz!Jn o (1 - t)z;n ,
while (3.2-4) simplifies to
(3.3-6) F(z) = 111 [ f ](z) = L[ f ](z) = ~ J f(t) dt, 0
where
= Jl [~]\dt 1 - tz
Using Lemma 1.2d again we have
Min Re q1(z) = Re q1(-1) = ( g1(-1) rl - 1 I z I =I
= 2[ 2 lo~ 2 - 1 ] - 1 = 0·294 .. ·. Combining all of our results we have proved the following theorem.
