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Some aspects of λ-weak convergence using difference operator
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DOI：10.1515/jaa-2024-0094.png)
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Abstract
En 中文
In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Delta iota and the de la Vall & eacute;e-Poussin mean, denoted as [ ( V , lambda ) w , Delta iota] m for m = 0 m=0 , 1, and infinity. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak lambda-statistical convergence, and generalized difference weak [ V , lambda ]-convergence.
Keywords:
lambda-convergence
lambda-statistical convergence
generalized difference operator
weak convergence
sequence spaces