{"paper":{"title":"Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amit Maji, Atanu Manna, P. D. Srivastava","submitted_at":"2013-07-19T17:24:18Z","abstract_excerpt":"This paper presents new sequence spaces $X(r, s, t, p ;\\Delta)$ for $X \\in \\{l_\\infty(p), c(p), c_0(p), l(p)\\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable paranorm. Furthermore, the $\\alpha$-, $\\beta$-, $\\gamma$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;\\Delta)$ to $X$. Finally, it is proved that the sequence space $l(r, s, t, p ;\\Delta)$ is rotund when $p_n>1$ for all $n$ and has the Kadec-Klee property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5884","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}