Affiliation:
1. Department of Mathematics , 72896 Tripura University , Suryamaninagar , Agartala-799022 , India
Abstract
Abstract
In this article, we introduced the idea of lacunary weak convergence of sequences defined by the class of Orlicz function. Various topological and algebraic properties, such as solidity, symmetry, and monotonicity, have been studied. To validate the failure instances, we gave appropriate examples and detailed discussions. Additionally, we have established some inclusion relationships between these spaces.
Reference12 articles.
1. S. Banach,
Théorie des opérations linéaires,
Monogr. Mat. 1,
Instytut Matematyczny PAN, Warszawa, 1932.
2. P. J. Dowari and B. C. Tripathy,
Lacunary difference sequences of complex uncertain variables,
Methods Funct. Anal. Topology 26 (2020), no. 4, 327–340.
3. P. J. Dowari and B. C. Tripathy,
Lacunary sequences of complex uncertain variables defined by Orlicz functions,
Proyecciones 40 (2021), no. 2, 355–370.
4. A. R. Freedman, J. J. Sember and M. Raphael,
Some Cesàro-type summability spaces,
Proc. Lond. Math. Soc. (3) 37 (1978), no. 3, 508–520.
5. J. Lindenstrauss and L. Tzafriri,
On Orlicz sequence spaces,
Israel J. Math. 10 (1971), 379–390.