A sequence-to-function analogue of the Hausdorff means for double sequences: the $[J,$ $f(x,\,y)]$ means

In this paper we extend the Jakimovski means to double sequences. We call the new means the <!-- MATH $[J,f(x,y)]$ --> means. We characterize such 's that give rise to regular and to totally regular <!-- MATH $[J,f(x,y)]$ --> means. We also give a necessary and sufficient condition for representability of a function as a double Laplace transform with a determining function of bounded variation in two variables.