For a sequence , define . Using this x, Kizmaz defined the sequence spaces , c( and as follows:
If E is any one of the above spaces, we have . The aim of the present paper is to extend the above sequence spaces to the sequence spaces of Maddox and Simons by considering a sequence of strictly positive numbers. For example if c(p) is the Maddox sequence space of convergent sequences, the author considers
Introducing the spaces , c(p) and , the author finds the first and second Köthe-Toeplitz duals of and asserts is perfect if and only if . The necessary and sufficient conditions for an infinite matrix to transform to c(, to and to c are obtained.