Affiliation:
1. Department of Mathematics , 418665 Chandigarh University , Mohali , 140301, Punjab , India
Abstract
Abstract
In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator
Δ
ı
ȷ
\Delta^{\jmath}_{\imath}
and the de la Vallée–Poussin mean, denoted as
[
(
V
,
λ
)
w
,
Δ
ı
ȷ
]
m
[(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m}
for
m
=
0
m=0
, 1, and ∞.
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 𝜆-statistical convergence, and generalized difference weak
[
V
,
λ
]
[\mathscr{V},\lambda]
-convergence.
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