Orlicz difference sequence spaces generated by infinite matrices and de la Vallée-Poussin mean of order α | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 24, Issue 4, 2016, Page 545-554 PDF (478.94 K) | ||||
| DOI: 10.1016/j.joems.2015.12.004 | ||||
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| Authors | ||||
| Bipan Hazarika1; Ayhan Esi2; Ayten Esi2; Karan Tamang3 | ||||
| 1Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, Arunachal Pradesh, India | ||||
| 2Adıyaman University, Department of Mathematics, Adıyaman, 02040, Turkey | ||||
| 3Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India | ||||
| Abstract | ||||
| In this paper we introduce the spaces V λ [A , M, , p] o , V λ [ A, M, , p ] and V λ [ A, M, , p ] ∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of S λ [ A, ] −convergence and derive some results between the spaces S λ [A , ] and V λ [ A, ] . Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space V α λ [ A, , p ] ∞ . Finally, we introduce the notion of almost λ-statistically-[ A , ]-convergence of order α or S α λ [ A, ] −convergence and obtain some inclusion relations between the set S α λ [A , ] and the space V α λ [ A, , p ] ∞ . | ||||
| Keywords | ||||
| Infinite matrix; Orlicz function; Statistical convergence; λ-sequence | ||||
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