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STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE

Year 2019, Volume: 2 Issue: 1, 1 - 7, 30.01.2019
https://doi.org/10.33773/jum.492367
https://izlik.org/JA79HM72TL

Abstract

In this work, we introduce the notions of statistical convergence

and lacunary statistical convergence of weight g in a locally solid Riesz space

and establish some inclusion relations.

References

  • [1] F. Riesz, Sur la decomposition des operations fonctionnelles lineaires, In Atti del CongressoInternazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, pp. 143-148 (1929).[2] H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, AfdeelingNatuurkunde, Proceedings of the Section of Sciences, 39, 647{657 (1936).[3] L. V. Kantorovich, Concerning the general theory of operations in partially ordered spaces,Dok. Akad. Nauk. SSSR 1, 271-274 (1936).[4] C. D. Aliprantis, O. Burkinshaw, Locally solid Riesz spaces with applications to economics,American Mathematical Society, Second Edition, USA, 105, (2003).[5] L. V. Kantorovich, Lineare halbgeordnete Raume, Recueil Mathmatique, 2(44), 121-168(1937).[6] W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces, American Elsevier Publishing Company,New York, (1971).[7] A. C. Zannen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, (1997).[8] H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solidRiesz spaces, Topology and its Applications, 159(7), 1887-1893 (2012).[9] M. Balcerzak, P. Das, M. Filipczak and J. Swaczyna Generalized kinds of density and theassociated ideals, Acta Mathematica Hungarica, 147(1), 97-115 (2015).[10] B. Hazarika, S. A. Mohiuddine and M. Mursaleen. Some inclusion results for lacunary sta-tistical convergence in locally solid Riesz spaces, Iranian Journal of Science and Technology,38(A1), 61-68 (2014).[11] R. Colak and C. A. Bektas. lambda-statistical convergence of order alpha, Acta Mathematica Scientia31(3), 953-959 (2011).

Year 2019, Volume: 2 Issue: 1, 1 - 7, 30.01.2019
https://doi.org/10.33773/jum.492367
https://izlik.org/JA79HM72TL

Abstract

References

  • [1] F. Riesz, Sur la decomposition des operations fonctionnelles lineaires, In Atti del CongressoInternazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, pp. 143-148 (1929).[2] H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, AfdeelingNatuurkunde, Proceedings of the Section of Sciences, 39, 647{657 (1936).[3] L. V. Kantorovich, Concerning the general theory of operations in partially ordered spaces,Dok. Akad. Nauk. SSSR 1, 271-274 (1936).[4] C. D. Aliprantis, O. Burkinshaw, Locally solid Riesz spaces with applications to economics,American Mathematical Society, Second Edition, USA, 105, (2003).[5] L. V. Kantorovich, Lineare halbgeordnete Raume, Recueil Mathmatique, 2(44), 121-168(1937).[6] W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces, American Elsevier Publishing Company,New York, (1971).[7] A. C. Zannen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, (1997).[8] H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solidRiesz spaces, Topology and its Applications, 159(7), 1887-1893 (2012).[9] M. Balcerzak, P. Das, M. Filipczak and J. Swaczyna Generalized kinds of density and theassociated ideals, Acta Mathematica Hungarica, 147(1), 97-115 (2015).[10] B. Hazarika, S. A. Mohiuddine and M. Mursaleen. Some inclusion results for lacunary sta-tistical convergence in locally solid Riesz spaces, Iranian Journal of Science and Technology,38(A1), 61-68 (2014).[11] R. Colak and C. A. Bektas. lambda-statistical convergence of order alpha, Acta Mathematica Scientia31(3), 953-959 (2011).
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şükran Konca

Ergin Genç This is me

Submission Date December 5, 2018
Acceptance Date January 14, 2019
Publication Date January 30, 2019
DOI https://doi.org/10.33773/jum.492367
IZ https://izlik.org/JA79HM72TL
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Konca, Ş., & Genç, E. (2019). STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. Journal of Universal Mathematics, 2(1), 1-7. https://doi.org/10.33773/jum.492367
AMA 1.Konca Ş, Genç E. STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. JUM. 2019;2(1):1-7. doi:10.33773/jum.492367
Chicago Konca, Şükran, and Ergin Genç. 2019. “STATISTICAL CONVERGENCE OF WEIGHT G IN A LOCALLY SOLID RIESZ SPACE”. Journal of Universal Mathematics 2 (1): 1-7. https://doi.org/10.33773/jum.492367.
EndNote Konca Ş, Genç E (January 1, 2019) STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. Journal of Universal Mathematics 2 1 1–7.
IEEE [1]Ş. Konca and E. Genç, “STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE”, JUM, vol. 2, no. 1, pp. 1–7, Jan. 2019, doi: 10.33773/jum.492367.
ISNAD Konca, Şükran - Genç, Ergin. “STATISTICAL CONVERGENCE OF WEIGHT G IN A LOCALLY SOLID RIESZ SPACE”. Journal of Universal Mathematics 2/1 (January 1, 2019): 1-7. https://doi.org/10.33773/jum.492367.
JAMA 1.Konca Ş, Genç E. STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. JUM. 2019;2:1–7.
MLA Konca, Şükran, and Ergin Genç. “STATISTICAL CONVERGENCE OF WEIGHT G IN A LOCALLY SOLID RIESZ SPACE”. Journal of Universal Mathematics, vol. 2, no. 1, Jan. 2019, pp. 1-7, doi:10.33773/jum.492367.
Vancouver 1.Şükran Konca, Ergin Genç. STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. JUM. 2019 Jan. 1;2(1):1-7. doi:10.33773/jum.492367