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

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 ⁢ ( 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)}

.