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

Research paper by Bipan Hazarika, Ayhan Esi, Ayten Esi, Karan Tamang

Indexed on: 23 Mar '16Published on: 22 Mar '16Published in: Journal of the Egyptian Mathematical Society



Abstract

In this paper we introduce the spaces <img height="25" border="0" style="vertical-align:bottom" width="128" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si1.gif">V^λ[A,M,Δ,p]o,<img height="25" border="0" style="vertical-align:bottom" width="115" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si2.gif">V^λ[A,M,Δ,p] and <img height="25" border="0" style="vertical-align:bottom" width="130" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si3.gif">V^λ[A,M,Δ,p]∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of <img height="21" border="0" style="vertical-align:bottom" width="82" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si4.gif">S^λ[A,Δ]−convergence and derive some results between the spaces <img height="21" border="0" style="vertical-align:bottom" width="67" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si5.gif">S^λ[A,Δ] and <img height="21" border="0" style="vertical-align:bottom" width="73" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si6.gif">V^λ[A,Δ]. Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space <img height="25" border="0" style="vertical-align:bottom" width="114" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si7.gif">V^λα[A,Δ,p]∞. Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α   or <img height="23" border="0" style="vertical-align:bottom" width="84" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si8.gif">S^λα[A,Δ]−convergence and obtain some inclusion relations between the set <img height="23" border="0" style="vertical-align:bottom" width="69" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si9.gif">S^λα[A,Δ] and the space <img height="25" border="0" style="vertical-align:bottom" width="114" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16300013-si7.gif">V^λα[A,Δ,p]∞.