CONVERGENCE OF COMPLEX UNCERTAIN TRIPLE SEQUENCE VIA METRIC OPERATOR, p-DISTANCE AND COMPLETE CONVERGENCE
Abstract
In this paper, we have introduced three new types of convergence concepts, namely convergence in p-distance, completely convergence and convergence in metric by considering triple sequences of complex uncertain variable. We have established the interrelationships among these notions and also with the existing ones. In this process, we have proven that the notions of convergence in metric and convergence in almost surely are equivalent in nature. Overall, this study presents a more complete scenario of interconnections between the notions of convergences initiated in different directions.
Keywords
Full Text:
PDFReferences
bibitem{ahm} Ahmadzade, H., Y. Sheng, and M. Esfahani. 2016. On the convergence of uncertain random sequences. textit{ Fuzzy Optimization and Decision Making} 16(2): 1-16.
bibitem{chen} Chen, X., X. Li, and D. Ralescu. (2014), A note on uncertain sequence. textit{ International Journal of Uncertainty, Fuzziness and Knowledge-Based System} 22(2): 305-314.
bibitem{chenet} Chen, X., Y. Ning, and X. Wang. 2016. Convergence of complex uncertain sequences. textit{ Journal of Intelligent $&$ Fuzzy System} 30(6): 3357-3366.
bibitem{thes} Das, B. 2021. A study on sequences of complex uncertain variable and matrix transformation. Doctoral Dissertation. NIT Agartala.
bibitem{dasjus} Das, B., B. C. Tripathy, and P. Debnath. 2021. Characterization of matrix classes transforming between almost sure convergent sequences of complex uncertain variables. textit{Journal of Uncertain Systems} 14(3): 1-12.
bibitem{dasfil} Das, B., B. C. Tripathy, P. Debnath, and B. Bhattacharya. 2021, Almost convergence of complex uncertain double sequences. textit{Filomat} 35(1): 61-78.
bibitem{dasamp} Das, B., B. C. Tripathy, P. Debnath, and B. Bhattacharya. 2020. Characterization of statistical convergence of complex uncertain double sequence. 2021. textit{ Analysis and Mathematical Physics} 10(4): 1-20
bibitem{dascstm} Das, B., B. C. Tripathy, P. Debnath, and B. Bhattacharya. 2021. Statistical convergence of complex uncertain triple sequence. textit{ Communications in Statistics Theory and Methods} doi: 10.1080/03610926.2020.1871016.
bibitem{dasthai} Das, B., B. Bhattacharya and B. C. Tripathy. Relation between convergence and almost convergence of complex uncertain sequences. 2025. textit{Kragujevac Journal of Mathematics}. 49(2):313-326.
bibitem{dasfil2} Das, B., B. C. Tripathy, P. Debnath, and B. Bhattacharya. 2020. Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences. textit{ Filomat} 34(14): 4907-4922.
bibitem{dasmfat} Das, B., B. C. Tripathy and P. Debnath. 2021. Results on matrix transformation of complex uncertain sequences via convergence in almost surely. textit{ Methods of Functional Analysis and Topology} 27(4): 320-327.
bibitem{dasnasa} Das, B., B. C. Tripathy, P. Debnath, J. Nath, and B. Bhattacharya. 2021. Almost convergence of complex uncertain triple sequences. textit{Proceedings of the National Academy of Sciences, India Section A: Physical Sciences} 91(2): 245-256.
bibitem{dat} Datta, D., and B. C. Tripathy. (2020), Convergence of complex uncertain double Sequences. textit{New Mathematics and Natural Computation} 16(3): 447-459.
bibitem{guo} Guo, H., and C. Xu. 2013. A necessary and sufficient condition of convergence in mean square for uncertain sequence. textit{Information, Japan} 16(2): 1091-1096.
bibitem{liu} Liu, B. 2007. textit{Uncertainty Theory}. 2nd Ed. Berlin: Springer-Verlag.
bibitem{nathijgs} Nath, J., B. C. Tripathy, B. Das and B. Bhattacharya. 2022. On strongly almost $lambda$-convergence and statistically almost $lambda$-convergence in the environment of uncertainty. textit{ International Journal of General Systems} 51(3): 262-276.
bibitem{peng} Peng, Z., and K. Iwamura. 2010. A sufficient and necessary condition of uncertainty distribution. textit{Journal of Interdisciplinary Mathematics} 13(3): 277-285.
bibitem{saha2} Roy, S., S. Saha, and B. C. Tripathy. 2020. Some results on p-distance and sequence of complex uncertain variables. textit{ Communications of the Korean Mathematical Society} 35(3): 907-916.
bibitem{saha1} Saha, S., B. C. Tripathy, and S. Roy. 2020, On almost convergent of complex uncertain sequences. textit{New Mathematics and Natural Computation} 16 (3): 573-580.
bibitem{nath} Tripathy, B. C., and P. K. Nath. 2017. Statistical convergence of complex uncertain sequences. textit{New Mathematics and Natural Computation} 13(3): 359-374.
bibitem{ye} Ye, T., and Y. Zhu. 2018. A metric on uncertain variables. textit{ International Journal for Uncertainty Quantification} 8(3): 251-266.
bibitem{you9} You, C. 2009. On the convergence of uncertain sequences. textit{ Mathematical and Computer Modelling} 49: 482-487.
bibitem{you16} You, C., and L. Yan. 2016. Relationships among convergence concepts of uncertain sequences. textit{ Computer Modelling and New Technologies} 20(3): 12-16.
DOI: https://doi.org/10.22190/FUMI220218026D
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)