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)} , ℓ ∞ ( G ) {\ell_{\infty}(G)} , and ℓ 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)} , ℓ ∞ ( G ) {\ell_{\infty}(G)} , and ℓ 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 ℓ p ( G ) {\ell_{p}(G)} .
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