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Some sequence spaces and almost convergence

Published online by Cambridge University Press:  09 April 2009

Sudarsan Nanda
Sudarsan Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela 769008, Orissa, India.
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Abstract

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In this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper is to introduce the spaces of strongly almost summable sequences which happen to be complete paranormed spaces under certain conditions. Some topological results, characterisation of strongly almost regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 446 - 455
Copyright
Copyright © Australian Mathematical Society 1976

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