N&#246;rlund methods of summability are studied as mappings from <mml:math alttext="$\ell _1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#8467;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> into <mml:math alttext="$\ell _1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#8467;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>. Those N&#246;rlund methods that map <mml:math alttext="$\ell _1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#8467;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> into <mml:math alttext="$\ell _1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#8467;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> are characterized. Inclusion results are given and a class of N&#246;rlund methods is shown to form an ordered abelian semigroup.

International Journal of Mathematics and Mathematical Sciences

An ordered set of Nörlund means

Abstract

Copyright