On Sequence Spaces Due to lth Order q-Difference Operator and its Spectrum

Yaying, Taja; Hazarika, Bipan; Mohiuddine, S. A.; Et, Mikail

doi:10.1007/s40995-023-01487-7

Iran J Sci

2023

DOI: 10.1007/s40995-023-01487-7

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On Sequence Spaces Due to lth Order q-Difference Operator and its Spectrum

Taja Yaying¹,

Bipan Hazarika

S. A. Mohiuddine

et al.

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2024

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Some aspects of 𝜆-weak convergence using difference operator

Sharma,

Kumari,

Kumar

2024

Journal of Applied Analysis

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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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Some aspects of 𝜆-weak convergence using difference operator

Sharma,

Kumari,

Kumar

2024

Journal of Applied Analysis

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On Sequence Spaces Due to lth Order q-Difference Operator and its Spectrum

Cited by 1 publication

References 26 publications

Some aspects of 𝜆-weak convergence using difference operator

Some aspects of 𝜆-weak convergence using difference operator

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