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

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Published/Copyright: August 3, 2024

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 ( G ) , ( G ) , and p ( G ) , where 1 p < . 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 ( G ) , ( G ) , and p ( G ) for values of p within the range of 1 p < . At last, we also prove existence theorem with example for infinite systems of differential equations in p ( G ) .

MSC 2020: 46A45; 40A05; 40C05

Acknowledgements

We thank the editor and referees for valuable comments and suggestions for improving the paper.

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Received: 2024-03-17
Revised: 2024-07-17
Accepted: 2024-07-19
Published Online: 2024-08-03
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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