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A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness

  • Muhammet Cihat Dağli EMAIL logo and Taja Yaying
Published/Copyright: April 24, 2024
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 32 Issue 1

Abstract

In this article, we introduce Fibo-Pascal sequence spaces P p F , 0 < p < ∞ , and P ∞ F through the utilization of the Fibo-Pascal matrix P F . We establish that both P p F and P ∞ F are BK-spaces, enjoying a linear isomorphism with the classical spaces ℓ p and ℓ ∞ , respectively. Further contributing to the depth of our investigation, we proceed to derive the Schauder basis of the space P p F , alongside an exhaustive computation of the α-, β-, and γ-duals for both spaces P p F and P ∞ F . Additionally, we undertake the task of characterizing certain classes of matrix mappings pertaining to the spaces P p F and P ∞ F . The final section of this study is dedicated to the meticulous characterization of compact operators acting in the spaces P 1 F , P p F , and P ∞ F by using Hausdorff measure of non-compactness.

Keywords: Fibo-Pascal sequence spaces; Schauder basis; matrix transformation; duals; compactness
MSC 2020: 46B45; 46A45; 40C05; 47B07

Acknowledgements

The authors thank the anonymous reviewer for making constructive comments that have improvised the presentation of the paper to a great extent.

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Received: 2023-10-18
Revised: 2023-12-18
Accepted: 2023-12-25
Published Online: 2024-04-24
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. A note on higher order Dirac operators in Clifford analysis
  3. Action of higher derivations on semiprime rings
  4. Demicompact linear operator. Essential pseudospectra and perturbation
  5. On the rotations and limit cycles of solutions to the basic system of equations
  6. On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
  7. A class of nontrivial simple examples of a non-D-space
  8. A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
  9. A property of the free Gaussian distribution
  10. The influence of c-subnormality subgroups on the structure of finite groups
  11. Wave propagation on hexagonal lattices
  12. Timelike zero mean curvature surfaces in ℝ1 4
  13. A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
  14. On corrected Simpson-type inequalities via local fractional integrals
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  16. On the singular directions of a holomorphic mapping in P n(ℂ)
  17. On minimal surfaces in ℍ2 × ℝ space
  18. Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
  19. Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
  20. On generalized derivations in factor rings
  21. Remarks on generalized derivations in factor rings
https://doi.org/10.1515/gmj-2024-2021
Keywords for this article
Fibo-Pascal sequence spaces; Schauder basis; matrix transformation; duals; compactness

Articles in the same Issue

  1. Frontmatter
  2. A note on higher order Dirac operators in Clifford analysis
  3. Action of higher derivations on semiprime rings
  4. Demicompact linear operator. Essential pseudospectra and perturbation
  5. On the rotations and limit cycles of solutions to the basic system of equations
  6. On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
  7. A class of nontrivial simple examples of a non-D-space
  8. A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
  9. A property of the free Gaussian distribution
  10. The influence of c-subnormality subgroups on the structure of finite groups
  11. Wave propagation on hexagonal lattices
  12. Timelike zero mean curvature surfaces in ℝ1 4
  13. A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
  14. On corrected Simpson-type inequalities via local fractional integrals
  15. Sobolev regularity for a class of local fractional new maximal operators
  16. On the singular directions of a holomorphic mapping in P n(ℂ)
  17. On minimal surfaces in ℍ2 × ℝ space
  18. Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
  19. Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
  20. On generalized derivations in factor rings
  21. Remarks on generalized derivations in factor rings
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