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On sequence spaces generated by binomial difference operator of fractional order

  • Taja Yaying und Bipan Hazarika EMAIL logo
Veröffentlicht/Copyright: 19. Juli 2019
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 69 Heft 4

Abstract

In this article we introduce binomial difference sequence spaces of fractional order α, bpr,s (Δ(α)) (1 ≤ p ≤ ∞) by the composition of binomial matrix, Br,s and fractional difference operator Δ(α), defined by (Δ(α)x)k = ∑i=0∞(−1)iΓ(α+1)i!Γ(α−i+1)xk−i. We give some topological properties, obtain the Schauder basis and determine the α, β and γ-duals of the spaces. We characterize the matrix classes (bpr,s(Δ(α)), Y), where Y ∈ {ℓ∞, c, c0, ℓ1} and certain classes of compact operators on the space bpr,s(Δ(α)) using Hausdorff measure of non-compactness. Finally, we give some geometric properties of the space bpr,s(Δ(α)) (1 < p < ∞).

MSC 2010: Primary 46A45; Secondary 46A35
Keywords: binomial difference sequence space; difference operator Δ(α); Schauder basis; α, β, γ-duals; matrix transformation; compact operator; Hausdorff measure of non-compactness; geometric properties

  1. (Communicated by Werner Timmerman)

Acknowledgement

The authors thank the referee for the valuable suggestions for improvement of the article.

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Received: 2018-08-07
Accepted: 2018-11-05
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0276
Schlagwörter für diesen Artikel
binomial difference sequence space; difference operator Δ(α); Schauder basis; α, β, γ-duals; matrix transformation; compact operator; Hausdorff measure of non-compactness; geometric properties

Artikel in diesem Heft

  1. Regular papers
  2. On the finite embeddability property for quantum B-algebras
  3. A dual Ramsey theorem for finite ordered oriented graphs
  4. On EMV-Semirings
  5. A nonsymmetrical matrix and its factorizations
  6. On weakly 𝓗-permutable subgroups of finite groups
  7. The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
  8. A geometrical version of Hardy-Rellich type inequalities
  9. On a Choquet-Stieltjes type integral on intervals
  10. Uniqueness of meromorphic functions sharing four small functions on annuli
  11. A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
  12. Functions of bounded variation related to domains bounded by conic sections
  13. Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
  14. Oscillatory criteria for the second order linear ordinary differential equations
  15. When deviation happens between rough statistical convergence and rough weighted statistical convergence
  16. The retraction of certain banach right modules associated to a character
  17. On sequence spaces generated by binomial difference operator of fractional order
  18. Some refinements of young type inequality for positive linear map
  19. On the Gromov-Hausdorff limit of metric spaces
  20. The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
  21. Hilbert algebras with supremum generated by finite chains
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