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The sequence space l(p)$l(p)$ having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space l(p)$l(p)$… Click to show full abstract
The sequence space l(p)$l(p)$ having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space l(p)$l(p)$ to the space |Eϕr|(p)$\vert E_{\phi }^{r} \vert (p)$ derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to l(p)$l(p)$. Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.
Journal Title: Journal of Inequalities and Applications
Year Published: 2018
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