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• W2054254310 abstract "We define a generalized Cesàro sequence space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathrm{ces}(p)$ id=E2><mml:mtext>ces</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$p=(p_{k})$ id=E3><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show that<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathrm{ces}(p)$ id=E4><mml:mtext>ces</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>is<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$k$ id=E5><mml:mi>k</mml:mi></mml:math>-nearly uniform convex (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$k$ id=E6><mml:mi>k</mml:mi></mml:math>-NUC) for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$kgeq 2$ id=E7><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math>when<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathrm{lim}_ {n rightarrow infty} mathrm{inf} p_{n}>1$ id=E8><mml:msub><mml:mtext>lim</mml:mtext><mml:mrow><mml:mi>n</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub><mml:mo>inf</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math>. Moreover, we also obtain that the Cesàro sequence space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathrm{ces}_{p}$ id=E9><mml:msub><mml:mtext>ces</mml:mtext><mml:mi>p</mml:mi></mml:msub></mml:math><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$(text{where} 1<p< infty)$ id=E10><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>where</mml:mtext><mml:mtext> </mml:mtext><mml:mn>1</mml:mn><mml:mo><</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>is<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$k$ id=E11><mml:mi>k</mml:mi></mml:math>-NUC,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$kR$ id=E12><mml:mi>k</mml:mi><mml:mi>R</mml:mi></mml:math>, NUC, and has a drop property." @default.
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• W2054254310 date "2003-01-01" @default.
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• W2054254310 title "Onk-nearly uniform convex property in generalized Cesàro sequence spaces" @default.
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