| | | |

## STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE

#### Şükran KONCA [1] , Ergin GENÇ [2]

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.

density, locally solid Riesz space, statistical convergence, topological vector space, weight
• [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).
Primary Language en Mathematics Research Article Author: Şükran KONCA (Primary Author)Institution: BITLIS EREN UNIVERSITYCountry: Turkey Author: Ergin GENÇInstitution: BITLIS EREN UNIVERSITYCountry: Turkey Application Date : December 5, 2018 Acceptance Date : January 14, 2019 Publication Date : January 30, 2019
 Bibtex @research article { jum492367, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2019}, volume = {2}, pages = {1 - 7}, doi = {10.33773/jum.492367}, title = {STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE}, key = {cite}, author = {Konca, Şükran and Genç, Ergin} } 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 . DOI: 10.33773/jum.492367 MLA Konca, Ş , Genç, E . "STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE" . Journal of Universal Mathematics 2 (2019 ): 1-7 Chicago Konca, Ş , Genç, E . "STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE". Journal of Universal Mathematics 2 (2019 ): 1-7 RIS TY - JOUR T1 - STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE AU - Şükran Konca , Ergin Genç Y1 - 2019 PY - 2019 N1 - doi: 10.33773/jum.492367 DO - 10.33773/jum.492367 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 1 EP - 7 VL - 2 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.492367 UR - https://doi.org/10.33773/jum.492367 Y2 - 2019 ER - EndNote %0 Journal of Universal Mathematics STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE %A Şükran Konca , Ergin Genç %T STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE %D 2019 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 2 %N 1 %R doi: 10.33773/jum.492367 %U 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 2019): 1-7 . https://doi.org/10.33773/jum.492367 AMA Konca Ş , Genç E . STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. JUM. 2019; 2(1): 1-7. Vancouver Konca Ş , Genç E . STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE. Journal of Universal Mathematics. 2019; 2(1): 1-7. IEEE Ş. Konca and E. Genç , "STATISTICAL CONVERGENCE OF WEIGHT g IN A LOCALLY SOLID RIESZ SPACE", Journal of Universal Mathematics, vol. 2, no. 1, pp. 1-7, Jan. 2019, doi:10.33773/jum.492367

Authors of the Article
[2]