Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NEW BANACH SPACES DEFINED BY THE DOMAIN OF RIESZ-FIBONACCI MATRIX

  • Received : 2021.04.02
  • Accepted : 2021.09.30
  • Published : 2021.12.30
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Abstract

The main object of this study is to introduce the spaces $c_0({\hat{F}^q)$ and $c({\hat{F}^q)$ derived by the matrix ${\hat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the 𝛼-, 𝛽-, 𝛾- duals of these spaces and give the characterization of matrix classes (${\Lambda}({\hat{F}^q)$, Ω) and (Ω, ${\Lambda}({\hat{F}^q)$) for 𝚲 ∈ {c0, c} and Ω ∈ {ℓ1, c0, c, ℓ∞}.

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Acknowledgement

The authors would like to thank the anonymous reviewers and the editor for their very helpful comments and valuable suggestions.

References

  1. A. Alotaibi, M. Mursaleen, B. AS Alamri and S. A. Mohiuddine, Compact operators on some Fibonacci difference sequence spaces, J. Inequal. Appl., 2015, 2015, Art. no. 203.
  2. Altay, B., Basar, F.: Some Paranormed Riesz Sequence Spaces of Non-absolute Type, Southeast Asian Bulletin of Mathematics 30 (4), (2006), 591-608.
  3. Altay, Bilal, and Feyzi Basar. Generalization of the sequence space l(p) derived by weighted mean, Journal of Mathematical Analysis and Applications 330 (1) (2007): 174-185. https://doi.org/10.1016/j.jmaa.2006.07.050
  4. Altay, B., Basar, F.: Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (1) (2007), 632-645. https://doi.org/10.1016/j.jmaa.2007.03.007
  5. Aydin, C., and F. Basar, Some new sequence spaces which include the spaces lp and l1, Demonstratio Mathematica 38 (3) (2005), 641-656. https://doi.org/10.1515/dema-2005-0313
  6. Basarir, M., Basar, F., Kara, EE., On the spaces of Fibonacci difference null and convergent sequences, arXiv:1309.0150v1 [math.FA], (2013).
  7. M. Candan, A new approach on the spaces of generalized Fibonacci difference null and convergent sequences, Math. Aeterna, 5 2015, 191-210.
  8. M. Candan and E. E. Kara, A study on topological and geometrical characteristics of new Banach sequence spaces, Gulf J. Math., 3 2015, 67-84.
  9. A. Das and B. Hazarika, Some new Fibonacci difference spaces of non-absolute type and compact operators, Linear Multilinear Algebra, 65 (2017), 2551-2573. https://doi.org/10.1080/03081087.2017.1278738
  10. S. Demiriz and C. Cakan, Some topological and geometrical properties of a new difference sequence space, Abstr. Appl. Anal., 2011 (2011), Art. ID 213878.
  11. S. Demiriz, E. E. Kara and M. Basarir, On the Fibonacci almost convergent sequence space and Fibonacci core, Kyungpook Math. J., 55 (2015), 355-372. https://doi.org/10.5666/KMJ.2015.55.2.355
  12. H. B. Ellidokuzoglu and S. Demiriz, Euler-Riesz difference sequence spaces, Turk. J. Math. Comput. Sci., 7 (2017), 63-72.
  13. S. Ercan , C.A. Bektas, On some sequence spaces of non-absolute type, Kragujevac J. Math.,38 (2014), 195-202. https://doi.org/10.5937/KgJMath1401195E
  14. S. Ercan , C.A. Bektas, On new convergent difference BK-spaces, J. Comput. Anal. Appl. 23 (5) (2017), 793-801.
  15. S. Ercan and C. A. Bektas, Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers, Linear Multilinear Algebra, 65 (2017), 909-921. https://doi.org/10.1080/03081087.2016.1215403
  16. S. Ercan, On λγ-Convergence and λγ-Boundedness, J. Adv. Phys., 7 (2018), 123-129. https://doi.org/10.1166/jap.2018.1399
  17. M. Ilkhan and E. E. Kara,Remarkable applications of measure of non-compactness for infinite system of differential equations, Appl. Appl. Math., 5 (2019), 1-12.
  18. Kara, E.E.: Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl. 38 (2013).
  19. E. E. Kara and S. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes, 16 (2015), 907-923. https://doi.org/10.18514/MMN.2015.1227
  20. Kara, EE., Ilkhan, M., On some Banach sequence spaces derived by a new band matrix, British Journal of Mathematics & Computer Science, 9 (2) (2015), 141-159. https://doi.org/10.9734/BJMCS/2015/17499
  21. Kara, EE., Ilkhan, M., Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra, 64 (11) (2016), 2208-2223. https://doi.org/10.1080/03081087.2016.1145626
  22. M. Ilkhan Kara and M. A. Bayrakdar, A study on matrix domain of Riesz-Euler totient matrix in the space of p-absolutely summable sequences, Commun. Adv. Math. Sci., 4 (1) (2021), 14-25.
  23. M. Ilkhan Kara and E. E. Kara, Matrix transformations and compact operators on Catalan sequence spaces, J. Math. Anal. Appl., 498 (1) (2021), Article 124925, 1-17.
  24. V. A. Khan, On Riesz-Musielak-Orlicz sequence spaces, Numer. Funct. Anal. Optim., 28 (2007), 883-895. https://doi.org/10.1080/01630560701404971
  25. V. A. Khan, R. K. A. Rababah, K. M. A. S. Alshlool, S. A. A. Abdullah and A. Ahmad, On ideal convergence Fibonacci difference sequence spaces, Adv. Difference Equ., 2018 (2018), Art. no. 199.
  26. V. A. Khan, K. M. A. S. Alshlool, A. A. H. Makharesh and S. A. A. Abdullah, On spaces of ideal convergent Fibonacci difference sequence defined by Orlicz function, Sigma J. Eng. Nat. Sci., 37 (2019), 143-154.
  27. Kizmaz, H.: On certain sequence spaces, Can. Math. Bull. 24(2) (1981), 169-176. https://doi.org/10.4153/CMB-1981-027-5
  28. M. Kirisci, The application domain of infinite matrices with algorithms, Univers. J. Math. Appl., 1 (2018), 1-9. https://doi.org/10.32323/ujma.376585
  29. Kirisci, M., Basar, F., Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl. 60 (2010), 1299-1309. https://doi.org/10.1016/j.camwa.2010.06.010
  30. S. A. Mohiuddine and B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat,31 (2017), 1827-1834. https://doi.org/10.2298/FIL1706827M
  31. Mursaleen, M., Generalized spaces of difference sequences, J. Math. Anal. Appl. 203 (3) (1996), 738-745. https://doi.org/10.1006/jmaa.1996.0409
  32. Mursaleen, M., F. Basar, and B. Altay., On the Euler sequence spaces which include the spaces lp and l∞ II, Nonlinear Analysis: Theory, Methods and Applications 65 (3) (2006), 707-717. https://doi.org/10.1016/j.na.2005.09.038
  33. Mursaleen, M., and Abdullah K. Noman., On some new sequence spaces of non-absolute type related to the spaces lp and l∞ I, Filomat 25 (2) (2011), 33-51. https://doi.org/10.2298/FIL1102033M
  34. H. Polat, Some new Pascal sequence spaces, Fundam. J. Math. Appl., 1 (2018), 61-68.
  35. Stieglitz, M., Tietz, H., Matrix transformationen von folgenraumen eine ergebnisubersicht, Math. Z. 154 (1977), 1-16. https://doi.org/10.1007/BF01215107
  36. T. Yaying and M. Ilkhan Kara, On sequence spaces defined by the domain of tribonacci matrix in c0 and c, Korean J. Math.,29 (1) (2021), 25-40. https://doi.org/10.11568/KJM.2021.29.1.25