Abstract
The notion of the generalized difference operator $$\Delta ^{(\alpha )}$$ of order $$\alpha $$ and the weighted mean operator G(u, v) are combined in the present article. Some related paranormed sequence spaces $$\ell _{\infty }(u,v;\Delta ^{(\alpha )},p),c_{0}(u,v;\Delta ^{(\alpha )},p),$$ $$c(u,v;\Delta ^{(\alpha )},p)$$ and $$ \ell (u,v;\Delta ^{(\alpha )},p)$$ , where $$\alpha $$ is a positive real number, are also introduced. Certain topological properties are studied and Schauder bases of these classes are determined. Also, the $$ {\mathbf {\alpha }}-,{\mathbf {\beta }}-$$ and $${\mathbf {\gamma }}-$$ duals of these spaces via matrix transformations are computed.
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Schedule a callMore From: Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
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