Research Article
BibTex RIS Cite
Year 2022, , 27 - 44, 01.03.2022
https://doi.org/10.36753/mathenot.816576

Abstract

References

  • Altay,B., Başar, F. and Mursaleen, M.: On the Euler sequence spaces which include the spaces $l_{p}$ and $l_{\infty}$ I. Inform. Sci. 176 (10), 1450-1462, (2005)
  • Başarır, M., Başar, F. and Kara, E. E.: On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences. Sarajevo J. Math. 12 (25), 167-182,(2016)
  • Bor, H.: On summability factors of infinite series, Tamkang J. Math. 16 (1), 13-20, (1985)
  • Djolovic, I. and Malkowsky, E.: Matrix transformations and compact operators on some new mth-order difference sequences. Appl. Math. Comput. 198 (2), 700-714, (2008)
  • FLett, T.M.: On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. Lond. Math. Soc. 7, 113-141, (1957)
  • Gökçe, F. and Sarıgöl, M.A.: On absolute Euler spaces and related matrix operators. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (in press).
  • Gökçe, F. and Sarıgöl, M.A.: Some matrix and compact operators of the absolute Fibonacci series spaces. Kragujevac J. Math. 44 (2), 273–286, (2020)
  • Hazar Güleç, G. C. : Characterization of some classes of compact and matrix operators on the sequence spaces of Cesaro matrices. Operators and Matrices, 13 (3), 809-822, (2019)
  • Jarrah, A.M. and Malkowsky, E.: Ordinary absolute and strong summability and matrix transformations. Filomat, 17, 59-78, (2003)
  • Kara, E. E. and Ilkhan, M.: Some properties of generalized Fibonacci sequence spaces. Linear Multilinear Algebra, 64 (11), 2208-2223, (2016)
  • Kara, E.E.: Some topological and geometrical properties of new Banach sequence spaces. J. Inequal. Appl. 2013 (1), 38, (2013)
  • Karakaş, M. and Karakaş, A.M.: A study on Lucas difference sequence spaces $l_{p}(\hat{E}(r,s))$ and $l_{\infty }(\hat{E}(r,s))$. Maejo International Journal of Science and Technology, 12, 70-78, (2018)
  • Koshy, T.: Fibonacci and Lucas numbers with applications (Vol. 51). JohnWiley and Sons, (2011)
  • Maddox, I.J.: Elements of functinal analysis, Cambridge University Press, London, New York, (1970)
  • [15] Malkowsky, E.: Compact matrix operators between some BK- spaces, in: M. Mursaleen (Ed.). Modern Methods of Analysis and Its Applications, Anamaya Publ., New Delhi, (2010), 86-120.
  • Malkowsky, E. and Rakocevic, V.: On matrix domains of triangles. Appl. Math. Comput., 189 (2), 1146-1163, (2007)
  • Malkowsky, E. and Rakocevic, V.: An introduction into the theory of sequence space and measures of noncompactness. Zb. Rad.(Beogr), 9 (17), 143-234, (2000)
  • Mohapatra, R.N. and Sarıgöl, M.A.: On matrix operators on the series spaces$\left|\bar N _{p}^{\theta}\right|_{k}$. Ukrain. Mat. Zh. 69 (11), 1524-1533, (2017)
  • Mursaleen, M.: Applied Summability Methods. Springer, Heidelberg, (2013)
  • Mursaleen, M. and Noman, A.K.: Compactness by the Hausdorff measure of noncompactness. Nonlinear Analysis: Theory, Methods & Applications, 73 (8), 2541-2557, (2010)
  • Mursaleen, M., Başar, F. and Altay, B.: On the Euler sequence spaces which include the spaces $l_{p}$ and $l_{\infty}$1 II. Nonlinear Anal. 65 (3), 707–717, (2006)
  • Rakocevic, V.: Measures of noncompactness and some applications. Filomat, 12 (2), 87-120, (1998)
  • Sarıgöl, M.A.: Spaces of Series Summable by Absolute Cesaro and Matrix Operators. Comm. Math Appl. 7 (1), 11-22, (2016)
  • Sarıgöl, M.A.: Extension of Mazhar’s theorem on summability factors. Kuwait J. Sci. 42 (3), 28-35, (2015)
  • Sarıgöl, M.A.: Matrix transformations on fields of absolute weighted mean summability. Studia Sci. Math. Hungar. 48 (3), 331-341, (2011)
  • Sarıgöl, M.A.: On the local properties of factored Fourier series. Appl. Math. Comput. 216 (11), 3386-3390, (2010)
  • Stieglitz, M. and Tietz, H.: Matrix transformationen von Folgenraumen. Eine Ergebnisübersicht. Math. Z., 154 (1), 1-16, (1977)
  • Sulaiman,W.T.: On summability factors of infinite series. Proc. Amer. Math. Soc. 115, 313- 317, (1992)
  • Wilansky, A.: Summability Through Functional Analysis, Mathematics Studies. 85. North Holland , Amsterdam, (1984)

Absolute Lucas Spaces with Matrix and Compact Operators

Year 2022, , 27 - 44, 01.03.2022
https://doi.org/10.36753/mathenot.816576

Abstract

The main purpose of this study is to introduce the absolute Lucas series spaces and to investigate their some algebraic and topological structure such as some inclusion relations, $BK-$ to this space, duals and Schauder basis. Also, the characterizations of matrix operators related to these space with their norms are given. Finally, by using Hausdorff measure of noncompactness, the necessary and sufficient conditions for a matrix operator on them to be compact are obtained.

References

  • Altay,B., Başar, F. and Mursaleen, M.: On the Euler sequence spaces which include the spaces $l_{p}$ and $l_{\infty}$ I. Inform. Sci. 176 (10), 1450-1462, (2005)
  • Başarır, M., Başar, F. and Kara, E. E.: On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences. Sarajevo J. Math. 12 (25), 167-182,(2016)
  • Bor, H.: On summability factors of infinite series, Tamkang J. Math. 16 (1), 13-20, (1985)
  • Djolovic, I. and Malkowsky, E.: Matrix transformations and compact operators on some new mth-order difference sequences. Appl. Math. Comput. 198 (2), 700-714, (2008)
  • FLett, T.M.: On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. Lond. Math. Soc. 7, 113-141, (1957)
  • Gökçe, F. and Sarıgöl, M.A.: On absolute Euler spaces and related matrix operators. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (in press).
  • Gökçe, F. and Sarıgöl, M.A.: Some matrix and compact operators of the absolute Fibonacci series spaces. Kragujevac J. Math. 44 (2), 273–286, (2020)
  • Hazar Güleç, G. C. : Characterization of some classes of compact and matrix operators on the sequence spaces of Cesaro matrices. Operators and Matrices, 13 (3), 809-822, (2019)
  • Jarrah, A.M. and Malkowsky, E.: Ordinary absolute and strong summability and matrix transformations. Filomat, 17, 59-78, (2003)
  • Kara, E. E. and Ilkhan, M.: Some properties of generalized Fibonacci sequence spaces. Linear Multilinear Algebra, 64 (11), 2208-2223, (2016)
  • Kara, E.E.: Some topological and geometrical properties of new Banach sequence spaces. J. Inequal. Appl. 2013 (1), 38, (2013)
  • Karakaş, M. and Karakaş, A.M.: A study on Lucas difference sequence spaces $l_{p}(\hat{E}(r,s))$ and $l_{\infty }(\hat{E}(r,s))$. Maejo International Journal of Science and Technology, 12, 70-78, (2018)
  • Koshy, T.: Fibonacci and Lucas numbers with applications (Vol. 51). JohnWiley and Sons, (2011)
  • Maddox, I.J.: Elements of functinal analysis, Cambridge University Press, London, New York, (1970)
  • [15] Malkowsky, E.: Compact matrix operators between some BK- spaces, in: M. Mursaleen (Ed.). Modern Methods of Analysis and Its Applications, Anamaya Publ., New Delhi, (2010), 86-120.
  • Malkowsky, E. and Rakocevic, V.: On matrix domains of triangles. Appl. Math. Comput., 189 (2), 1146-1163, (2007)
  • Malkowsky, E. and Rakocevic, V.: An introduction into the theory of sequence space and measures of noncompactness. Zb. Rad.(Beogr), 9 (17), 143-234, (2000)
  • Mohapatra, R.N. and Sarıgöl, M.A.: On matrix operators on the series spaces$\left|\bar N _{p}^{\theta}\right|_{k}$. Ukrain. Mat. Zh. 69 (11), 1524-1533, (2017)
  • Mursaleen, M.: Applied Summability Methods. Springer, Heidelberg, (2013)
  • Mursaleen, M. and Noman, A.K.: Compactness by the Hausdorff measure of noncompactness. Nonlinear Analysis: Theory, Methods & Applications, 73 (8), 2541-2557, (2010)
  • Mursaleen, M., Başar, F. and Altay, B.: On the Euler sequence spaces which include the spaces $l_{p}$ and $l_{\infty}$1 II. Nonlinear Anal. 65 (3), 707–717, (2006)
  • Rakocevic, V.: Measures of noncompactness and some applications. Filomat, 12 (2), 87-120, (1998)
  • Sarıgöl, M.A.: Spaces of Series Summable by Absolute Cesaro and Matrix Operators. Comm. Math Appl. 7 (1), 11-22, (2016)
  • Sarıgöl, M.A.: Extension of Mazhar’s theorem on summability factors. Kuwait J. Sci. 42 (3), 28-35, (2015)
  • Sarıgöl, M.A.: Matrix transformations on fields of absolute weighted mean summability. Studia Sci. Math. Hungar. 48 (3), 331-341, (2011)
  • Sarıgöl, M.A.: On the local properties of factored Fourier series. Appl. Math. Comput. 216 (11), 3386-3390, (2010)
  • Stieglitz, M. and Tietz, H.: Matrix transformationen von Folgenraumen. Eine Ergebnisübersicht. Math. Z., 154 (1), 1-16, (1977)
  • Sulaiman,W.T.: On summability factors of infinite series. Proc. Amer. Math. Soc. 115, 313- 317, (1992)
  • Wilansky, A.: Summability Through Functional Analysis, Mathematics Studies. 85. North Holland , Amsterdam, (1984)
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fadime Gökçe 0000-0003-1819-3317

Publication Date March 1, 2022
Submission Date October 26, 2020
Acceptance Date February 17, 2021
Published in Issue Year 2022

Cite

APA Gökçe, F. (2022). Absolute Lucas Spaces with Matrix and Compact Operators. Mathematical Sciences and Applications E-Notes, 10(1), 27-44. https://doi.org/10.36753/mathenot.816576
AMA Gökçe F. Absolute Lucas Spaces with Matrix and Compact Operators. Math. Sci. Appl. E-Notes. March 2022;10(1):27-44. doi:10.36753/mathenot.816576
Chicago Gökçe, Fadime. “Absolute Lucas Spaces With Matrix and Compact Operators”. Mathematical Sciences and Applications E-Notes 10, no. 1 (March 2022): 27-44. https://doi.org/10.36753/mathenot.816576.
EndNote Gökçe F (March 1, 2022) Absolute Lucas Spaces with Matrix and Compact Operators. Mathematical Sciences and Applications E-Notes 10 1 27–44.
IEEE F. Gökçe, “Absolute Lucas Spaces with Matrix and Compact Operators”, Math. Sci. Appl. E-Notes, vol. 10, no. 1, pp. 27–44, 2022, doi: 10.36753/mathenot.816576.
ISNAD Gökçe, Fadime. “Absolute Lucas Spaces With Matrix and Compact Operators”. Mathematical Sciences and Applications E-Notes 10/1 (March 2022), 27-44. https://doi.org/10.36753/mathenot.816576.
JAMA Gökçe F. Absolute Lucas Spaces with Matrix and Compact Operators. Math. Sci. Appl. E-Notes. 2022;10:27–44.
MLA Gökçe, Fadime. “Absolute Lucas Spaces With Matrix and Compact Operators”. Mathematical Sciences and Applications E-Notes, vol. 10, no. 1, 2022, pp. 27-44, doi:10.36753/mathenot.816576.
Vancouver Gökçe F. Absolute Lucas Spaces with Matrix and Compact Operators. Math. Sci. Appl. E-Notes. 2022;10(1):27-44.

Cited By

Tribonacci-Lucas Dizi Uzayları
Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.21597/jist.1154099

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.