# Rate of P-convergence over equivalence classes of double sequence spaces

Rate of P-convergence over equivalence classes of double sequence spaces This paper presents multidimensional characterizations of equivalence classes of double sequences. These characterizations will be analyzed by presenting theorems of the following type: If A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \;{\rm equivalent \; to}\; b\}}$$ then there exists a $${b^{\prime} \in S^{\prime\prime}_{0}}$$ such that b converges faster than b′ and A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \; {\rm equivalent \; to}\; b^{\prime}\}.}$$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Rate of P-convergence over equivalence classes of double sequence spaces

, Volume 16 (4) – Sep 28, 2011
11 pages

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Potential Theory; Operator Theory; Fourier Analysis; Econometrics; Calculus of Variations and Optimal Control; Optimization
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0143-7
Publisher site
See Article on Publisher Site

### Abstract

This paper presents multidimensional characterizations of equivalence classes of double sequences. These characterizations will be analyzed by presenting theorems of the following type: If A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \;{\rm equivalent \; to}\; b\}}$$ then there exists a $${b^{\prime} \in S^{\prime\prime}_{0}}$$ such that b converges faster than b′ and A is convergent preserving over $${\{x \in S^{\prime\prime}_{0} : x \; {\rm equivalent \; to}\; b^{\prime}\}.}$$

### Journal

PositivitySpringer Journals

Published: Sep 28, 2011

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