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We consider a large class of arithmetical functions generated by Dirichlet series satisfying a functional equation with gamma factors. Our objective is to state some 12 results for the average order of these arithmetical functions. Our objective here is to state some B-theorems on the average order of a class of arithmetical functions. We indicate very briefly the class of arithmetical functions under consideration. For a more complete description, see [4]. Let {a(n)} and {b(n)} be two sequences of complex numbers, not identically zero. Let {Xw} and {fxn} be two strictly increasing sequences of positive numbers tending to <*>. Put s = a+it with cr and t both real and suppose that

On the average order of some arithmetical functions