In this paper the sequence spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) are linearly isomorphic to spaces c 0 (p), c(p), ∞ (p) and (p), respectively. Besides this, the α−, β − and γ−duals of the spaces b r,s 0 (p), b r,s c (p), and b r,s (p) have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices (b r,s 0 (p) : µ), (b r,s c (p) : µ) and (b r,s (p) : µ) have been characterized, where µ is one of the sequence spaces ∞ , c and c 0 and derives the other characterizations for the special cases of µ.
In this paper the sequence spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p) are linearly isomorphic to spaces c 0 (p), c(p), ∞ (p) and (p), respectively. Besides this, the α−, β − and γ−duals of the spaces b r,s 0 (p), b r,s c (p), and b r,s (p) have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices (b r,s 0 (p) : µ), (b r,s c (p) : µ) and (b r,s (p) : µ) have been characterized, where µ is one of the sequence spaces ∞ , c and c 0 and derives the other characterizations for the special cases of µ.
<abstract><p>In this study, we construct the spaces of $ q $-difference sequences of order $ m $. We obtain some inclusion relations, topological properties, Schauder basis and alpha, beta and gamma duals of the newly defined spaces. We characterize certain matrix classes from the newly defined spaces to any one of the spaces $ c_0, c, \ell_\infty $ and $ \ell_p $.</p></abstract>
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