We consider continuously differentiable means, say C1-means. As for quasi-arithmetic means Qf (x1, . . . ,xn), we need an assumption that f has no stationary points so that Qf might be continuouslyâ€¦ (More)

Suppose A is a Banach algebra without order. We show that an approximate multiplier T : A â†’ A is an exact multiplier. We also consider an approximate multiplier T on a Banach algebra which need notâ€¦ (More)

* Correspondence: sin-ei@emperor. yz.yamagata-u.ac.jp Toho University, Yamagata University (Professor Emeritus), Chiba 273-0866, Japan Full list of author information is available at the end of theâ€¦ (More)

*Correspondence: sin_ei1@yahoo.co.jp 1Department of Information Sciences, Toho University, Funabashi, 274-8501, Japan Full list of author information is available at the end of the article Abstractâ€¦ (More)

LetX be a set with a binary operation â—¦ such that, for each x, y, z âˆˆ X, either x â—¦y â—¦z x â—¦z â—¦y, or zâ—¦ xâ—¦y xâ—¦ zâ—¦y . We show the superstability of the functional equation g xâ—¦y g x g y . Moreâ€¦ (More)

When A is a subalgebra of the commutative Banach algebra C0(X) of all continuous complex-valued functions on a locally compact Hausdorff space X, the spatial numerical range of element of A can beâ€¦ (More)