α-, β- and γ-duals of the sequence spaces formed by a regular matrix of Tetranacci numbers

Author:

Khan Izhar Ali1ORCID,Meitei Mayanglambam Udoy1

Affiliation:

1. Department of Mathematics , School of Basic Sciences , 30071 CSJM University , Kanpur - 208024 , India

Abstract

Abstract The primary objective of this paper is to create a novel infinite Toeplitz matrix by leveraging Tetranacci numbers. This matrix serves as the foundation for defining new sequence spaces denoted as c 0 ( G ) {c_{0}(G)} , c ( G ) {c(G)} , ( G ) {\ell_{\infty}(G)} , and p ( G ) {\ell_{p}(G)} , where 1 p < {1\leq p<\infty} . By utilizing this newly constructed matrix, the paper also explores and examines various algebraic and topological properties inherent to the sequence spaces c 0 ( G ) {c_{0}(G)} , c ( G ) {c(G)} , ( G ) {\ell_{\infty}(G)} , and p ( G ) {\ell_{p}(G)} for values of p within the range of 1 p < {1\leq p<\infty} . At last, we also prove existence theorem with example for infinite systems of differential equations in p ( G ) {\ell_{p}(G)} .

Publisher

Walter de Gruyter GmbH

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