Concerning semi-ordered linear spaces, L. Kantorovitch 1 gave originally two different concepts of convergence, that is, order convergence and star convergence. One of the authors introduced two other concepts, that is, dilatator convergence in 2 and individual convergence in 3, which are essentially equivalent to each other. Combining these concepts, we also obtain star-individual convergence in 4. In this paper we want to discuss these concepts of convergence and their combinations more

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... atically. In the sequel we will use the terminologies and notations in the book 4. Let R be a continuous semi-ordered linear space. We consider the order convergence basic, that is, for a sequence aeR (,----0, 1, 2, ..