Some generalizations of the space bυp of p-bounded variation sequences

The spaces b upsilon(p) and b upsilon(infinity) of sequences of p-bounded variation have recently been introduced by Basar and Altay [F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (1) (2003) 136-147], where 1 < p < infinity. In the present paper, the sequence spaces b upsilon(u, p) and b upsilon(infinity)(u, p) of non-absolute type have been defined and it has been proved that the spaces b upsilon(u, p) and b upsilon(infinity)(u, p) are linearly isomorphic to the spaces l(p) and l(infinity)(p) of Maddox, respectively. Besides this, the alpha-, beta- and gamma-duals of the spaces b upsilon(u, p) and b upsilon(infinity)(u, p) have been computed and the basis of the space b upsilon(u, p) has been constructed. The classes (b upsilon(u, p) : l(infinity)) and (b upsilon(u, p) : c) of infinite matrices have been characterized and the characterizations of some other classes have also been derived by means of a given basic lemma. The final section of the paper has been devoted to some consequences about the rotundity of the space b upsilon(u, p). (c) 2006 Elsevier Ltd. All rights reserved.