Orlicz difference sequence spaces generated by infinite matrices and de la Vallée-Poussin mean of order α

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• 作者：Bipan Hazarika ; ^a ; ^{bh_rgu@yahoo.co.in" class="auth_mail" title="E-mail the corresponding author} ; Ayhan Esi^b ; ^{aesi23@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ayten Esi^b ; ^{aytenesi@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Karan Tamang^c ; ^{karanthingh@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Infinite matrix ; Orlicz function ; Statistical convergence ; λ-sequence
• 刊名：Journal of the Egyptian Mathematical Society
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：4
• 页码：545-554
• 全文大小：478 K

文摘

In this paper we introduce the spaces ${\widehat{V}}_{\lambda }{[A,M,\Delta ,p]}_o,$${\widehat{V}}_{\lambda }[A,M,\Delta ,p]$ and ${\widehat{V}}_{\lambda }{[A,M,\Delta ,p]}_{\infty }$ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of ${\widehat{S}}_{\lambda }[A,\Delta ]-$convergence and derive some results between the spaces ${\widehat{S}}_{\lambda }[A,\Delta ]$ and ${\widehat{V}}_{\lambda }[A,\Delta ].$ Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space 79567fc4e06bde59">${\widehat{V}}_{\lambda }^{\alpha }{[A,\Delta ,p]}_{\infty }.$ Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α   or ${\widehat{S}}_{\lambda }^{\alpha }[A,\Delta ]-$convergence and obtain some inclusion relations between the set ${\widehat{S}}_{\lambda }^{\alpha }[A,\Delta ]$ and the space 79567fc4e06bde59">${\widehat{V}}_{\lambda }^{\alpha }{[A,\Delta ,p]}_{\infty }.$