In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 $B:=x^{-\beta }{\prod }_{j=1}^m(x(d/dx)+\beta {\gamma }_j)$, β>0, ${\gamma }_j\in R$, j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms...