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I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES

Year 2019, , 22 - 31, 30.01.2019
https://doi.org/10.33773/jum.492457

Abstract

An ideal $I$ is a family of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this  paper, we introduce the notions of ideal versions of weighted lacunary statistical $\tau$-convergence, statistical $\tau$-Cauchy, weighted lacunary $\tau$-boundedness of sequences in locally solid Riesz spaces endowed with the topology $\tau$. We also prove some topological results related to these concepts in locally solid Riesz space.

References

  • \bibitem{1} F. Riesz, Sur la decomposition des operations fonctionnelles lineaires. In Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, pp. 143-148 (1929). \bibitem{2} H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, Afdeeling Natuurkunde, Proceedings of the Section of Sciences 39, 647-657 (1936). \bibitem{3} L. V. Kantorovich, Concerning the general theory of operations in partially ordered spaces, Dok. Akad. Nauk. SSSR 1, 271-274 (1936). \bibitem{4} C. D. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces with applications to economics, (No. 105). American Mathematical Soc., (2003). \bibitem{5} L. V. Kantorovich, Lineare halbgeordnete Raume, Rec. Math. 2, 121-168 (1937). \bibitem{6} W. A. Luxemburg and A. C. Zaanen, Riesz spaces. Vol. I, (1971). \bibitem{7} A. C. Zannen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, 1997. \bibitem{8} H. Fast, Sur la convergence statistique, Colloq. Math., 2, 241-244 (1951). \bibitem{9} H. Steinhaus, Sur la convergence ordinate et la convergence asymptotique, Colloq. Math., 2, 73-84 (1951). \bibitem{14} H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solid Riesz spaces, Topology and its Applications, 159 (7) , 1887-1893 (2012). \bibitem{15} V. Karakaya and T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33 (1), 219-223 (2009). \bibitem{17} M. Ba\c{s}ar{\i}r and \c{S}. Konca, On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence, Arab Journal of Mathematical Sciences 20 (2), 250-263 (2014). \bibitem{18} M. Ba\c{s}ar{\i}r and \c{S}. Konca, "Weighted lacunary statistical convergence in locally solid Riesz spaces." Filomat 28 (10), 2059-2067 2014. \bibitem{19} P. Kostyrko, T. Salat, and W. Wilczynski, I-convergence,Real Analysis Exchange, 26 (2), 669-686 (2000-2001). \bibitem{20} B. Hazarika, Ideal convergence in locally solid Riesz spaces. Filomat, 28 (4), 797-809 (2014). \bibitem{21} B. K. Lahiri and P. Das, $I$ and $I^*$convergence in topological space, Mathematica Bohemica, 130 (2), 153-160 (2005). \bibitem{22} B. Hazarika, On ideal convergence in topological groups. Department of Mathematics Northwest University, 7 (4), 42-48 (2011). \bibitem{23} \c{S}. Konca ,E. Gen\c{c} and S. Ekin, Ideal version of weighted lacunary statistical convergence of sequences of order, Journal of Mathematical Analysis 7 (6), (2016). \bibitem{24} S. A. Mohiuddine, B. Hazarika and M. Mursaleen, Some inclusion results for lacunary statistical convergence in locally solid Riesz spaces, Iranian Journal of Science and Technology 38. A1 61 (2014). \bibitem{28} S. A.Mohiuddine and M. A. Alghamdi, Statistical summability through a lacunary sequence in locally solid Riesz spaces. Journal of Inequalities and Applications, 2012 (1), 225 (2012).
Year 2019, , 22 - 31, 30.01.2019
https://doi.org/10.33773/jum.492457

Abstract

References

  • \bibitem{1} F. Riesz, Sur la decomposition des operations fonctionnelles lineaires. In Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, pp. 143-148 (1929). \bibitem{2} H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, Afdeeling Natuurkunde, Proceedings of the Section of Sciences 39, 647-657 (1936). \bibitem{3} L. V. Kantorovich, Concerning the general theory of operations in partially ordered spaces, Dok. Akad. Nauk. SSSR 1, 271-274 (1936). \bibitem{4} C. D. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces with applications to economics, (No. 105). American Mathematical Soc., (2003). \bibitem{5} L. V. Kantorovich, Lineare halbgeordnete Raume, Rec. Math. 2, 121-168 (1937). \bibitem{6} W. A. Luxemburg and A. C. Zaanen, Riesz spaces. Vol. I, (1971). \bibitem{7} A. C. Zannen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, 1997. \bibitem{8} H. Fast, Sur la convergence statistique, Colloq. Math., 2, 241-244 (1951). \bibitem{9} H. Steinhaus, Sur la convergence ordinate et la convergence asymptotique, Colloq. Math., 2, 73-84 (1951). \bibitem{14} H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solid Riesz spaces, Topology and its Applications, 159 (7) , 1887-1893 (2012). \bibitem{15} V. Karakaya and T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33 (1), 219-223 (2009). \bibitem{17} M. Ba\c{s}ar{\i}r and \c{S}. Konca, On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence, Arab Journal of Mathematical Sciences 20 (2), 250-263 (2014). \bibitem{18} M. Ba\c{s}ar{\i}r and \c{S}. Konca, "Weighted lacunary statistical convergence in locally solid Riesz spaces." Filomat 28 (10), 2059-2067 2014. \bibitem{19} P. Kostyrko, T. Salat, and W. Wilczynski, I-convergence,Real Analysis Exchange, 26 (2), 669-686 (2000-2001). \bibitem{20} B. Hazarika, Ideal convergence in locally solid Riesz spaces. Filomat, 28 (4), 797-809 (2014). \bibitem{21} B. K. Lahiri and P. Das, $I$ and $I^*$convergence in topological space, Mathematica Bohemica, 130 (2), 153-160 (2005). \bibitem{22} B. Hazarika, On ideal convergence in topological groups. Department of Mathematics Northwest University, 7 (4), 42-48 (2011). \bibitem{23} \c{S}. Konca ,E. Gen\c{c} and S. Ekin, Ideal version of weighted lacunary statistical convergence of sequences of order, Journal of Mathematical Analysis 7 (6), (2016). \bibitem{24} S. A. Mohiuddine, B. Hazarika and M. Mursaleen, Some inclusion results for lacunary statistical convergence in locally solid Riesz spaces, Iranian Journal of Science and Technology 38. A1 61 (2014). \bibitem{28} S. A.Mohiuddine and M. A. Alghamdi, Statistical summability through a lacunary sequence in locally solid Riesz spaces. Journal of Inequalities and Applications, 2012 (1), 225 (2012).
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şükran Konca

Ergin Genç This is me

Publication Date January 30, 2019
Submission Date December 5, 2018
Acceptance Date January 16, 2019
Published in Issue Year 2019

Cite

APA Konca, Ş., & Genç, E. (2019). I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. Journal of Universal Mathematics, 2(1), 22-31. https://doi.org/10.33773/jum.492457
AMA Konca Ş, Genç E. I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. JUM. January 2019;2(1):22-31. doi:10.33773/jum.492457
Chicago Konca, Şükran, and Ergin Genç. “I-WEIGHTED LACUNARY STATISTICAL Tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES”. Journal of Universal Mathematics 2, no. 1 (January 2019): 22-31. https://doi.org/10.33773/jum.492457.
EndNote Konca Ş, Genç E (January 1, 2019) I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. Journal of Universal Mathematics 2 1 22–31.
IEEE Ş. Konca and E. Genç, “I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES”, JUM, vol. 2, no. 1, pp. 22–31, 2019, doi: 10.33773/jum.492457.
ISNAD Konca, Şükran - Genç, Ergin. “I-WEIGHTED LACUNARY STATISTICAL Tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES”. Journal of Universal Mathematics 2/1 (January 2019), 22-31. https://doi.org/10.33773/jum.492457.
JAMA Konca Ş, Genç E. I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. JUM. 2019;2:22–31.
MLA Konca, Şükran and Ergin Genç. “I-WEIGHTED LACUNARY STATISTICAL Tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES”. Journal of Universal Mathematics, vol. 2, no. 1, 2019, pp. 22-31, doi:10.33773/jum.492457.
Vancouver Konca Ş, Genç E. I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. JUM. 2019;2(1):22-31.