On New Difference Sequence Space and Their Generalised Almost Statistical Convergence
DOI:
https://doi.org//10.32628/IJSRST207144Keywords:
Banach limits, Banach statistical limit functional, Linear functional, Almost convergence, Generalised almost convergence, Generalised almost statistical convergence.Abstract
The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. We also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.
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