The authors establish some propositions about the nonexistence of complex zeros of the functions , and , for in general complex. Some bounds for the purely imaginary zeros of the above functions are also obtained assuming their existence. These bounds for the purely imaginary zeros of are as follows:
where , , , , , are the real and imaginary parts of , and . The authors use these bounds to measure the purely imaginary zeros of .
The results proved by the authors generalize some of the results given earlier by E. K. Ifantis, P. D. Siafarikas and C. B. Kouris [J. Math. Anal. Appl. 104, 454-466 (1984; Zbl 0558.34006)].