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On Absolute Cesa ́ro Series Space And Certain Matrix Transformations

Year 2022, Volume: 12 Issue: 2, 560 - 570, 15.12.2022
https://doi.org/10.31466/kfbd.1036644

Abstract

On recent paper, the paranormed space |C_(λ,μ) |(p) which is defined as the domain of Cesa ́ro matrix in the Maddox’s space l(p) has been introduced and studied in (Gökçe and Sarıgöl, 2019). In this study, some characterizations of matrix operators from the Absolute Cesa ́ro series space |C_(λ,μ) |(p) to the classical sequence spaces c,c_0,l_∞ are given. Also, it is shown that the matrix operators between the absolute Cesa ́ro series space and the spaces c,c_0,l_∞ are bounded operators. Finally, certain results are obtained as a special case.

References

  • Gökçe, F. (2021). Compact and Matrix Operators on the Space |N ̅_P^θ |_k. Fundamental Journal of Mathematics and Applications 4(2), 124-133.
  • Gökçe, F., Sarıgöl, M.A. (2020). Series spaces derived from absolute Fibonacci summability and matrix transformations. Bollettino dell'Unione Matematica Italiana, 13, 29-38.
  • Gökçe, F., Sarıgöl, M.A. (2019). Generalization of the absolute Ces`aro space and some matrix transformations. Numerical Functional Analysis and Optimization, 40, 1039-1052.
  • Gökçe, F., Sarıgöl, M.A. (2019a). Extension of Maddox’s space l(μ) with Nörlund means. Asian-European Journal of Mathematics 12.06 (2019), 2040005.
  • Gökçe, F., Sarıgöl, M.A. (2018). A new series space |N ̅_P^θ |(μ) and matrix transformations with applications. Kuwait Journal of Science, 45(4), 1-8.
  • Grosse – Erdmann, K.G. (1993). Matrix transformations between the sequence spaces of Maddox, Journal of Mathematical Analysis and Applications, 180(1), 223-238.
  • Güleç, G. C. H. (2020). Applications of measure of noncompactness in the series spaces of generalized absolute Cesaro means. Karadeniz Fen Bilimleri Dergisi, 10(1), 60-73.
  • Maddox, I.J. (1969). Some properties of paranormed sequence spaces, Journal of the London Mathematical Society, 1, 316-322.
  • Maddox, I.J. (1968). Paranormed sequence spaces generated by infinite matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 64, 335-340.
  • Maddox, I.J. (1967). Spaces of strongly summable sequences, The Quarterly Journal of Mathematics 18, 345 -355
  • Malkowsky, E., Rakocevic, V. (2007). On matrix domains of triangles. Applied Mathematics and Computation ,189(2), 1146- 1163.
  • Malkowsky, E., Rakocevic, V. (2000). An introduction into the theory of sequence space and measures of noncompactness, Zbornik Radova.(Beograd), 9(17), 143-234.
  • Sarıgöl, M.A. (2016). Spaces of series summable by absolute Cesa ́ro and matrix operators, Communications in Mathematics and Applications, 7, 11-22.
  • Wilansky, A., (1984). Summability through Functional Analysis. Mathematical Studies 85, North–Holland, Amsterdam.
  • Zengin Alp, P., Ilkhan, M. (2019). On the difference sequence space l_p (T ̂^q). Math. Sci. Appl. E- Notes, 7(2), 161-173.

Mutlak Cesa ́ro Seri Uzayı Ve Bazı Matris Dönüşümleri

Year 2022, Volume: 12 Issue: 2, 560 - 570, 15.12.2022
https://doi.org/10.31466/kfbd.1036644

Abstract

Son zamanlarda, Cesa ́ro matrisinin, l(p) Maddox uzayı içinde toplama alanı olarak tanımlanan |C_(λ,μ) |(p) paranormlu uzayı tanıtılmış ve çalışılmıştır, (Gökçe ve Sarıgöl, 2019). Bu çalışmada, |C_(λ,μ) |(p) mutlak Cesa ́ro seri uzayından c,c_0,l_∞ klasik dizi uzaylarına tanımlanan matris operatörlerin karakterizasyonları verilmiştir. Ayrıca mutlak Cesa ́ro seri uzayları ve c,c_0,l_∞ uzayları arasındaki matris operatörlerin sınırlı lineer operatör olduğu gösterilmiştir. Son olarak, özel seçimlerle bazı sonuçlar elde edilmiştir.

References

  • Gökçe, F. (2021). Compact and Matrix Operators on the Space |N ̅_P^θ |_k. Fundamental Journal of Mathematics and Applications 4(2), 124-133.
  • Gökçe, F., Sarıgöl, M.A. (2020). Series spaces derived from absolute Fibonacci summability and matrix transformations. Bollettino dell'Unione Matematica Italiana, 13, 29-38.
  • Gökçe, F., Sarıgöl, M.A. (2019). Generalization of the absolute Ces`aro space and some matrix transformations. Numerical Functional Analysis and Optimization, 40, 1039-1052.
  • Gökçe, F., Sarıgöl, M.A. (2019a). Extension of Maddox’s space l(μ) with Nörlund means. Asian-European Journal of Mathematics 12.06 (2019), 2040005.
  • Gökçe, F., Sarıgöl, M.A. (2018). A new series space |N ̅_P^θ |(μ) and matrix transformations with applications. Kuwait Journal of Science, 45(4), 1-8.
  • Grosse – Erdmann, K.G. (1993). Matrix transformations between the sequence spaces of Maddox, Journal of Mathematical Analysis and Applications, 180(1), 223-238.
  • Güleç, G. C. H. (2020). Applications of measure of noncompactness in the series spaces of generalized absolute Cesaro means. Karadeniz Fen Bilimleri Dergisi, 10(1), 60-73.
  • Maddox, I.J. (1969). Some properties of paranormed sequence spaces, Journal of the London Mathematical Society, 1, 316-322.
  • Maddox, I.J. (1968). Paranormed sequence spaces generated by infinite matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 64, 335-340.
  • Maddox, I.J. (1967). Spaces of strongly summable sequences, The Quarterly Journal of Mathematics 18, 345 -355
  • Malkowsky, E., Rakocevic, V. (2007). On matrix domains of triangles. Applied Mathematics and Computation ,189(2), 1146- 1163.
  • Malkowsky, E., Rakocevic, V. (2000). An introduction into the theory of sequence space and measures of noncompactness, Zbornik Radova.(Beograd), 9(17), 143-234.
  • Sarıgöl, M.A. (2016). Spaces of series summable by absolute Cesa ́ro and matrix operators, Communications in Mathematics and Applications, 7, 11-22.
  • Wilansky, A., (1984). Summability through Functional Analysis. Mathematical Studies 85, North–Holland, Amsterdam.
  • Zengin Alp, P., Ilkhan, M. (2019). On the difference sequence space l_p (T ̂^q). Math. Sci. Appl. E- Notes, 7(2), 161-173.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Fadime Gökçe 0000-0003-1819-3317

Publication Date December 15, 2022
Published in Issue Year 2022 Volume: 12 Issue: 2

Cite

APA Gökçe, F. (2022). On Absolute Cesa ́ro Series Space And Certain Matrix Transformations. Karadeniz Fen Bilimleri Dergisi, 12(2), 560-570. https://doi.org/10.31466/kfbd.1036644