Lacunary statistical convergence of complex uncertain variables
DOI:
https://doi.org/10.5269/bspm.52688Resumen
In this paper, we introduce the notion of lacunary statistical convergence for the sequences of complex uncertain variables for almost sure, mean, measure and distribution. We investigate some of the basic properties of the notion. We have established relation between these notions.
Referencias
1. Chen, X., Ning, Y. and Wang, X., Convergence of complex uncertain sequences, Jour Intell Fuzzy Syst., 30(6), 3357-3366, (2016). https://doi.org/10.3233/IFS-152083
2. Connor, J. S., The statistical and strong p-Ces'aro convergence of sequences, Analysis, 8, 47-63, (1988). https://doi.org/10.1524/anly.1988.8.12.47
3. Dutta, A., Esi, A. and Tripathy, B.C., On lacunary p-absolutely summable fuzzy real-valued double sequence space, Demon. Math., 47(3), 652-661, (2014). https://doi.org/10.2478/dema-2014-0052
4. Fast, H., Sur la convergence statistique, Colloq. Math., 2(3-4), 241-244, (1951). https://doi.org/10.4064/cm-2-3-4-241-244
5. Freedman, A. R., Sember, J. J. and Raphael, M., Some Cesaro-type summability spaces, Proc. Lond. Math Soc., 37(3), 508-520, (1978). https://doi.org/10.1112/plms/s3-37.3.508
6. Fridy, J. A., On statistically convergence, Analysis 5, 301-313, (1985). https://doi.org/10.1524/anly.1985.5.4.301
7. Fridy, J. A. and Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160, 43-51, (1993). https://doi.org/10.2140/pjm.1993.160.43
8. Liu, B., Some Research Problems in Uncertainty Theory, Jour. Uncertain Syst., 3(1), 3-10, (2009).
9. Liu, B.,Why is there a need for Uncertainty Theory?., Jour. Uncertain Syst., 6(1), 3-10, (2012).
10. Liu, B., Uncertainity Theory, 5th Ed.(2016), Springer-Verlag, Berlin.
11. Nath, P. K. and Tripathy, B. C., Convergent complex uncertain sequences defined by Orlicz function, Annals of the University of Craiova, Mathematics and Computer Science Series, 46(1), 139-149, (2019).
12. Nath, P. K. and Tripathy, B. C., Statistical convergence of complex uncertain sequences defined by Orlicz function,Proyecciones J. Math., 39(2), 301-315, (2020). https://doi.org/10.22199/issn.0717-6279-2020-02-0019
13. Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2), 139-150, (1980).
14. Schoenberg, I. J., The integrability of some functions and related summability methods, Amer. Math. Mont., 66,361-375, (1959). https://doi.org/10.2307/2308747
15. Tripathy, B. C. and Mahanta, S., On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Math. Appl. Sin. (Eng. Ser.), 20(2), 231-238, (2004). https://doi.org/10.1007/s10255-004-0163-1
16. Tripathy, B. C. and Et, M.,On generalized difference lacunary statistical convergence, Stud Univ Babes-Bolyai Math, 50(1), 119-130,(2005).
17. Tripathy, B. C. and Baruah, A., Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), 565-574, (2010). https://doi.org/10.5666/KMJ.2010.50.4.565
18. Tripathy, B. C. and Dutta, H., On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary ∆nm-statistical convergence, Analele Stiintifice ale Universitatii Ovidius, Seria Matematica, 20(1), 417-430, (2012). https://doi.org/10.2478/v10309-012-0028-1
19. Tripathy, B. C., Hazarika, B. and Choudhary, B., Lacunary I-convergent sequences, Kyungpook Math. J., 52(4), 473-482, (2012). https://doi.org/10.5666/KMJ.2012.52.4.473
20. Tripathy, B. C. and Dutta, A. J., Lacunary bounded variation sequence of fuzzy real numbers, Jour. .Intell. Fuzzy Syst., 24(1), 185-189, (2013). https://doi.org/10.3233/IFS-2012-0544
21. Tripathy, B. C. and Dutta, A.J., Lacunary I-convergent sequences of fuzzy real numbers, Proyecciones J. Math., 34(3), 205-218, (2015). https://doi.org/10.4067/S0716-09172015000300001
22. Tripathy, B. C. and Nath, P., Statistical convergence of complex uncertain sequences, New Mathematics and Natural Computing, 13(3), 359-374, (2017). https://doi.org/10.1142/S1793005717500090
23. Tripathy, B. C. and Dowari, P. J., Norlund and Riesz mean of sequence of complex uncertain variables, Filomat, 32(8), 2875-2881, (2018). https://doi.org/10.2298/FIL1808875T
24. You, C., On the convergence of uncertain sequences, Math. Comput. Model., 49(4), 482-487, (2009). https://doi.org/10.1016/j.mcm.2008.07.007
25. Saha, S., Tripathy, B. C. and Roy, S., Some Results on p-distance and sequence of complex uncertain variables, Commun. Korean Math. Soc., 35(3), 907-916, (2020).
2. Connor, J. S., The statistical and strong p-Ces'aro convergence of sequences, Analysis, 8, 47-63, (1988). https://doi.org/10.1524/anly.1988.8.12.47
3. Dutta, A., Esi, A. and Tripathy, B.C., On lacunary p-absolutely summable fuzzy real-valued double sequence space, Demon. Math., 47(3), 652-661, (2014). https://doi.org/10.2478/dema-2014-0052
4. Fast, H., Sur la convergence statistique, Colloq. Math., 2(3-4), 241-244, (1951). https://doi.org/10.4064/cm-2-3-4-241-244
5. Freedman, A. R., Sember, J. J. and Raphael, M., Some Cesaro-type summability spaces, Proc. Lond. Math Soc., 37(3), 508-520, (1978). https://doi.org/10.1112/plms/s3-37.3.508
6. Fridy, J. A., On statistically convergence, Analysis 5, 301-313, (1985). https://doi.org/10.1524/anly.1985.5.4.301
7. Fridy, J. A. and Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160, 43-51, (1993). https://doi.org/10.2140/pjm.1993.160.43
8. Liu, B., Some Research Problems in Uncertainty Theory, Jour. Uncertain Syst., 3(1), 3-10, (2009).
9. Liu, B.,Why is there a need for Uncertainty Theory?., Jour. Uncertain Syst., 6(1), 3-10, (2012).
10. Liu, B., Uncertainity Theory, 5th Ed.(2016), Springer-Verlag, Berlin.
11. Nath, P. K. and Tripathy, B. C., Convergent complex uncertain sequences defined by Orlicz function, Annals of the University of Craiova, Mathematics and Computer Science Series, 46(1), 139-149, (2019).
12. Nath, P. K. and Tripathy, B. C., Statistical convergence of complex uncertain sequences defined by Orlicz function,Proyecciones J. Math., 39(2), 301-315, (2020). https://doi.org/10.22199/issn.0717-6279-2020-02-0019
13. Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2), 139-150, (1980).
14. Schoenberg, I. J., The integrability of some functions and related summability methods, Amer. Math. Mont., 66,361-375, (1959). https://doi.org/10.2307/2308747
15. Tripathy, B. C. and Mahanta, S., On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Math. Appl. Sin. (Eng. Ser.), 20(2), 231-238, (2004). https://doi.org/10.1007/s10255-004-0163-1
16. Tripathy, B. C. and Et, M.,On generalized difference lacunary statistical convergence, Stud Univ Babes-Bolyai Math, 50(1), 119-130,(2005).
17. Tripathy, B. C. and Baruah, A., Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), 565-574, (2010). https://doi.org/10.5666/KMJ.2010.50.4.565
18. Tripathy, B. C. and Dutta, H., On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary ∆nm-statistical convergence, Analele Stiintifice ale Universitatii Ovidius, Seria Matematica, 20(1), 417-430, (2012). https://doi.org/10.2478/v10309-012-0028-1
19. Tripathy, B. C., Hazarika, B. and Choudhary, B., Lacunary I-convergent sequences, Kyungpook Math. J., 52(4), 473-482, (2012). https://doi.org/10.5666/KMJ.2012.52.4.473
20. Tripathy, B. C. and Dutta, A. J., Lacunary bounded variation sequence of fuzzy real numbers, Jour. .Intell. Fuzzy Syst., 24(1), 185-189, (2013). https://doi.org/10.3233/IFS-2012-0544
21. Tripathy, B. C. and Dutta, A.J., Lacunary I-convergent sequences of fuzzy real numbers, Proyecciones J. Math., 34(3), 205-218, (2015). https://doi.org/10.4067/S0716-09172015000300001
22. Tripathy, B. C. and Nath, P., Statistical convergence of complex uncertain sequences, New Mathematics and Natural Computing, 13(3), 359-374, (2017). https://doi.org/10.1142/S1793005717500090
23. Tripathy, B. C. and Dowari, P. J., Norlund and Riesz mean of sequence of complex uncertain variables, Filomat, 32(8), 2875-2881, (2018). https://doi.org/10.2298/FIL1808875T
24. You, C., On the convergence of uncertain sequences, Math. Comput. Model., 49(4), 482-487, (2009). https://doi.org/10.1016/j.mcm.2008.07.007
25. Saha, S., Tripathy, B. C. and Roy, S., Some Results on p-distance and sequence of complex uncertain variables, Commun. Korean Math. Soc., 35(3), 907-916, (2020).
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2022-12-21
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