Generalized N$\Ddot{O}$rlund Means of Complex Uncertain Variables
Generalized N$\Ddot{O}$rlund Means of Complex Uncertain Variables
Résumé
In this article we have introduced the notion of generalized N$\ddot{o}$rlund mean associated with sequence of complex uncertain variables. The generalized N$\ddot{o}$rlund mean is defined based on two N$\ddot{o}$rlund means. We have established some results on the relationship of two regular N$\ddot{o}$rlund
means. The focus is to show that there is a third mean, which is stronger than the two N$\ddot{o}$rlund means
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Références
\bibitem{tripathy2018norlund} Tripathy B. C. and Dowari P. J., \emph{N\"{o}rlund and Riesz mean of sequence of complex uncertain variables}, Filomet, \textbf{32}(2018), no. 8, 2875-2881.\\
\bibitem{dowari2020} P.J. Dowari and B.C. Tripathy, Lacunary difference sequences of complex uncertain variables, Methods of Functional Analysis and Topology, 26(4)(2020), 327-340. https://doi.org/10.31392/MFAT-npu26\_4.2020.04 \\
\bibitem{das2020} Das, B., Tripathy, B. C., Debnath, P., and Bhattacharya, B., \emph{Study of matrix transformation ofuniformly almost surely convergent complex uncertain sequences}, Filomat, 34(2020), no. 14, 4907-4922. \\
\bibitem{liu2009some} Liu B., \emph{Some Research Problems in Uncertainty Theory}, Journal of Uncertain Systems, \textbf{3}(2009), no. 1, 3-10. \\
\bibitem{liu2016} Liu B., \emph{Uncertainty Theory}, Springer-Verlag, 5th Edition, Berlin, 2016.\\
\bibitem{you2009convergence} You C., \emph{On the convergence of uncertain sequences}, Mathematical and Computer Modeling, \textbf{49}(2009), no. 3-4, 482-487. \\
\bibitem{datta2019} Datta D. and Tripathy B. C., \emph{convergence of complex uncertain double sequences}, New Mathematics and Natural Computation, 16(3)(2020), 447-459.
\bibitem{peterson1966}Petersen, G. M., \emph{Regular Matrix Transformations}, McGraw-Hill, 1966. \\
\bibitem{debnath2019} Debnath P. and Tripathy B. C., \emph{On a new class of complex uncertain sequences related to the $\ell_p(\Gamma)$ space}, New Mathematics and Natural Computation, 17(1), (2021), 91-103. doi.no. 10.1142/S1793005721500058. \\
\bibitem{nath2019convergence} Nath P. K. and Tripathy B. C., \emph{Convergent complex uncertain sequences defined by Orlicz function}, Annals of the University of Craiova, Mathematics and Computer Science Series, \textbf{46}(2019), no. 1, 139-149. \\
\bibitem{nath2020} P.K. Nath and B.C. Tripathy, Statistical convergence of complex uncertain sequences defined by Orlicz function, Proyecciones J. Math., 39(2), (2020), 301-315. \\
\bibitem{chen2016convergence} Chen X., Ning Y. and Wang X., \emph{Convergence of complex uncertain sequences}, Jour. Intell. fuzzy syst., \textbf{30}(2016), no. 6, 3357-3366. \\
\bibitem{liu2010expected} Liu Y. and Ha M., \emph{Expected value of function of uncertain variables }, Jour. Uncertain Syst., \textbf{4}(2010), no. 3, 181-186. \\
\bibitem{peng2012} Peng Z., \emph{Complex uncertain variable}, Doctoral Dissertation, Tsinghua University, 2012. \\
\bibitem{tripathy2017} B.C. Tripathy and P.K. Nath: Statistical convergence of complex uncertain sequences, New Mathematics and Natural Computation, 13(3)(2017), 359-374. \\
\bibitem{tripathy2021} S. Saha, B.C. Tripathy, S. Roy, \emph{On Riesz mean of complex uncertain sequences}, Journal of Mathematical Analysis and Applications, 2021, 499(2), 125017, DOI: 10.1016/j.jmaa.2021.125017
\bibitem{dowari2020} P.J. Dowari and B.C. Tripathy, Lacunary difference sequences of complex uncertain variables, Methods of Functional Analysis and Topology, 26(4)(2020), 327-340. https://doi.org/10.31392/MFAT-npu26\_4.2020.04 \\
\bibitem{das2020} Das, B., Tripathy, B. C., Debnath, P., and Bhattacharya, B., \emph{Study of matrix transformation ofuniformly almost surely convergent complex uncertain sequences}, Filomat, 34(2020), no. 14, 4907-4922. \\
\bibitem{liu2009some} Liu B., \emph{Some Research Problems in Uncertainty Theory}, Journal of Uncertain Systems, \textbf{3}(2009), no. 1, 3-10. \\
\bibitem{liu2016} Liu B., \emph{Uncertainty Theory}, Springer-Verlag, 5th Edition, Berlin, 2016.\\
\bibitem{you2009convergence} You C., \emph{On the convergence of uncertain sequences}, Mathematical and Computer Modeling, \textbf{49}(2009), no. 3-4, 482-487. \\
\bibitem{datta2019} Datta D. and Tripathy B. C., \emph{convergence of complex uncertain double sequences}, New Mathematics and Natural Computation, 16(3)(2020), 447-459.
\bibitem{peterson1966}Petersen, G. M., \emph{Regular Matrix Transformations}, McGraw-Hill, 1966. \\
\bibitem{debnath2019} Debnath P. and Tripathy B. C., \emph{On a new class of complex uncertain sequences related to the $\ell_p(\Gamma)$ space}, New Mathematics and Natural Computation, 17(1), (2021), 91-103. doi.no. 10.1142/S1793005721500058. \\
\bibitem{nath2019convergence} Nath P. K. and Tripathy B. C., \emph{Convergent complex uncertain sequences defined by Orlicz function}, Annals of the University of Craiova, Mathematics and Computer Science Series, \textbf{46}(2019), no. 1, 139-149. \\
\bibitem{nath2020} P.K. Nath and B.C. Tripathy, Statistical convergence of complex uncertain sequences defined by Orlicz function, Proyecciones J. Math., 39(2), (2020), 301-315. \\
\bibitem{chen2016convergence} Chen X., Ning Y. and Wang X., \emph{Convergence of complex uncertain sequences}, Jour. Intell. fuzzy syst., \textbf{30}(2016), no. 6, 3357-3366. \\
\bibitem{liu2010expected} Liu Y. and Ha M., \emph{Expected value of function of uncertain variables }, Jour. Uncertain Syst., \textbf{4}(2010), no. 3, 181-186. \\
\bibitem{peng2012} Peng Z., \emph{Complex uncertain variable}, Doctoral Dissertation, Tsinghua University, 2012. \\
\bibitem{tripathy2017} B.C. Tripathy and P.K. Nath: Statistical convergence of complex uncertain sequences, New Mathematics and Natural Computation, 13(3)(2017), 359-374. \\
\bibitem{tripathy2021} S. Saha, B.C. Tripathy, S. Roy, \emph{On Riesz mean of complex uncertain sequences}, Journal of Mathematical Analysis and Applications, 2021, 499(2), 125017, DOI: 10.1016/j.jmaa.2021.125017
Publiée
2025-12-04
Numéro
Rubrique
Research Articles
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