Generalized lacunary \({\Delta^m}\)-statistically convergent sequences of fuzzy numbers using a modulus function. (English) Zbl 1301.40002
Summary: In this paper, we introduce the space of lacunary strongly \(\Delta^m_{(p)}\)-summable sequences of fuzzy numbers and discuss relations between \(\Delta^m\)-statistically convergent sequences and lacunary \(\Delta^m\)-statistically convergent sequences of fuzzy numbers. We also study inclusion relations using different arbitrary lacunary sequences.
MSC:
| 40A05 | Convergence and divergence of series and sequences |
| 40C05 | Matrix methods for summability |
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 26E50 | Fuzzy real analysis |
Keywords:
fuzzy number; modulus function; lacunary \(\Delta^m\)-statistical convergence; lacunary refinementReferences:
| [1] | doi:10.1016/S0019-9958(65)90241-X · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X |
| [2] | doi:10.1016/0165-0114(89)90222-4 · Zbl 0707.54003 · doi:10.1016/0165-0114(89)90222-4 |
| [3] | doi:10.1007/s10114-005-0719-x · Zbl 1123.46007 · doi:10.1007/s10114-005-0719-x |
| [4] | doi:10.1007/s10496-011-0021-y · Zbl 1249.46005 · doi:10.1007/s10496-011-0021-y |
| [5] | doi:10.1016/S0165-0114(98)00031-1 · Zbl 0937.40002 · doi:10.1016/S0165-0114(98)00031-1 |
| [6] | doi:10.1016/j.ins.2003.08.014 · Zbl 1038.40001 · doi:10.1016/j.ins.2003.08.014 |
| [7] | doi:10.1016/j.camwa.2006.03.025 · Zbl 1127.40005 · doi:10.1016/j.camwa.2006.03.025 |
| [8] | doi:10.5666/KMJ.2010.50.4.565 · Zbl 1229.40007 · doi:10.5666/KMJ.2010.50.4.565 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
