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 n id="mmlsi1" class="mathmlsrc">View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si1.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=295375d2dc44a70325402a9f675e469a">lass="imgLazyJSB inlineImage" height="25" width="128" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si1.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">V^ver>λ[A,M,Δ,p]o,n>n>n>n id="mmlsi2" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si2.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=c4cf384ed20d7922fa52403ba747da39">lass="imgLazyJSB inlineImage" height="25" width="115" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si2.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">V^ver>λ[A,M,Δ,p]n>n>n> and n id="mmlsi3" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si3.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=51c3076d8d85326ab331bf70d0a8746f">lass="imgLazyJSB inlineImage" height="25" width="130" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si3.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">verflow="scroll">ver accent="true">V^ver>λ[A,M,Δ,p]&infin;n>n>n> generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of n id="mmlsi4" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si4.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=a3f5631adf33482855a4d3d78b03fce2">lass="imgLazyJSB inlineImage" height="21" width="82" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si4.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">S^ver>λ[A,Δ]&minus;n>n>n>convergence and derive some results between the spaces n id="mmlsi5" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si5.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=defe14c11e3822231319fa4bb939df8c">lass="imgLazyJSB inlineImage" height="21" width="67" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si5.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">S^ver>λ[A,Δ]n>n>n> and n id="mmlsi6" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si6.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=17ef01a2c1c2daebcbfbf3c316fc30ac">lass="imgLazyJSB inlineImage" height="21" width="73" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si6.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">V^ver>λ[A,Δ].n>n>n> Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach&ndash;Saks property of the new space n id="mmlsi7" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si7.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=e3d498fab25b83db79567fc4e06bde59">lass="imgLazyJSB inlineImage" height="25" width="114" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si7.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">V^ver>λα[A,Δ,p]&infin;.n>n>n> Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α   or n id="mmlsi8" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si8.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=f2d91ec07edae1a27b2ed6664ba97247">lass="imgLazyJSB inlineImage" height="23" width="84" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si8.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">S^ver>λα[A,Δ]&minus;n>n>n>convergence and obtain some inclusion relations between the set n id="mmlsi9" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si9.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=13f28c79d0754c186a3263ac0a84bd1c">lass="imgLazyJSB inlineImage" height="23" width="69" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si9.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">S^ver>λα[A,Δ]n>n>n> and the space n id="mmlsi7" class="mathmlsrc">lass="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16300013&_mathId=si7.gif&_user=111111111&_pii=S1110256X16300013&_rdoc=1&_issn=1110256X&md5=e3d498fab25b83db79567fc4e06bde59">lass="imgLazyJSB inlineImage" height="25" width="114" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16300013-si7.gif"><noscript>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">noscript>n class="mathContainer hidden">n class="mathCode">nt="true">V^ver>λα[A,Δ,p]&infin;.n>n>n>