Limit properties of quasi-arithmetic means

Limit properties of the class {M-g lambda}(lambda is an element of (0,infinity)) of all quasi-arithmetic means generated by A-powers of a given generator g are studied. Special types of generators of quasi-arithmetic means that uniquely correspond to the additive generators of continuous Archimedean t-norms or t-conorms are considered. It is shown that for lambda --> infinity, the situation is similar to that for t-norms and t-conorms [6]. For lambda --> 0(+), the limit operators are quasi-geometric means. Finally, the limit properties of the class {M-g alpha}(alpha is an element of (0,infinity)) of all quasi-arithmetic means generated by functions g(alpha), g(alpha)(x) = g(x(alpha)) are investigated. (C) 2001 Elsevier Science B.V. All rights reserved.