Abstract
By e p r , we mean the space of all sequences whose Euler transforms of order r are in the sequence spaces ℓ p and ℓ ∞ (see [B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces ℓ p and ℓ ∞ I, Inform. Sci. (2005) (in press)]), where 1 ≤ p < ∞ . In the present paper, we essentially characterize the classes ( e p r : ℓ ∞ ) , ( e 1 r : ℓ p ) and ( e p r : f ) of infinite matrices for 1 < p ≤ ∞ and give the characterizations of some other matrix mappings from the space e p r to the Euler, Riesz, difference, etc., sequence spaces, by means of a given basic lemma. We devote the final section of the paper to examining some geometric properties of the space e p r .
Published Version
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