Lacunary sequences of complex uncertain variables defined by Orlicz functions




Almost convergent sequences, Complex uncertain variable, Orlicz function, Lacunary sequence


Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

Author Biographies

Pranab Jyoti Dowari, Tripura University

Dept. of Mathematics, 

Binod Chandra Tripathy, Tripura University

Dept. of Mathematics.


A. R. Freedman, J. J. Sember, and M. Raphael, “Some Cesàro-Type Summability Spaces”, Proceedings of the London Mathematical Society, vol. s3-37, no. 3, pp. 508–520, 1978. doi: 10.1112/plms/s3-37.3.508

B. C. Tripathy and S. Mahanta, “On a class of sequences related to the ?p space defined by Orlicz functions”, Soochow journal of mathematics, vol. 29, no. 4, pp. 379-391, 2003.

B. C. Tripathy and S. Mahanta, “On a class of generalized lacunary difference sequence spaces defined by Orlicz functions”, Acta mathematicae applicatea sinica, english series, vol. 20, no. 2, pp. 231-238, 2004, doi: 10.1007/s10255-004-0163-1

B. C. Tripathy and A. Esi, ”Generalized lacunary difference sequence spaces defined by Orlicz functions”, Matimyás matematika, vol. 28, no. 1-3, pp. 50-57, 2005.

B. C. Tripathy and P. J. Dowari, “Nörlund and Riesz mean of sequence of complex uncertain variables”, Filomat, vol. 32, no. 8, pp. 2875-2881, 2018, doi: 10.2298/FIL1808875T

B. C. Tripathy and P. Nath, “Statistical convergence of complex uncertain sequences”, New mathematics and natural computing, vol. 13, no. 2, pp. 359-374, 2017, doi: 10.1142/S1793005717500090

B. Liu, “Some research problems in uncertainty theory”, Journal uncertain system, vol. 3, no. 1, pp. 3-10, 2009. [On line]. Available:

B. Liu, ”Why is there a need for uncertainty theory?”, Journal uncertain system, vol. 6, no. 1, pp. 3-10, 2012. [On line]. Available:

B. Liu, Uncertainty theory, 4th ed. Berlin: Springer, 2015, doi: 10.1007/978-3-662-44354-5

C. You, “On the convergence of uncertain sequences”, Mathematical and computer modelling, vol. 49, no. 3-4, pp. 482-487, 2009, doi: 10.1016/j.mcm.2008.07.007

G. G. Lorentz, “A contribution to the theory of divergent sequences”, Acta mathematica, vol. 80, pp. 167-190, 1948, doi: 10.1007/BF02393648

J. P. King, “Almost summable sequences”, Proceeding American Mathematical Society, vol. 16, pp. 1219-1225, 1966, doi: 10.1090/S0002-9939-1966-0201872-6

P. J. Dowari and B.C. Tripathy, “Lacunary convergence of sequences of complex uncertain variables”, Boletim da Sociedade Paranaense de Matemática (Online), Preprint, 2020, doi: 10.5269/bspm.52688

P. K. Kamthan and M. Gupta, Sequence spaces and series. New York, NY: M. Dekker, 1981.

S. D. Parashar and B. Choudhary, “Sequence spaces defined by Orlicz functions”, Indian journal of pure and applied mathematics, vol. 25, no. 4, pp. 419-428, 1994. [On line]. Available:

X. Chen, Y. Ning, and X. Wang, ”Convergence of complex uncertain sequences”, Journal of intelligent & fuzzy systems, vol. 30, no. 6, pp. 3357-3366, 2016, doi: 10.3233/IFS-152083



How to Cite

P. J. Dowari and B. C. Tripathy, “Lacunary sequences of complex uncertain variables defined by Orlicz functions”, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 355-370, Mar. 2021.




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