Some vector valued multiplier difference sequence spaces defined by a sequence of Orlicz functions

Dutta H.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 2.

Abstract:
In this article we introduce some new difference sequence spaces with a real 2-normed linear space as base space and which are defined using a sequence of Orlicz functions, a bounded sequence of positive real numbers and a sequence of non-zero reals as multiplier sequence. We show that these spaces are complete paranormed spaces when the base space is a 2-Banach space and investigate these spaces for solidity, symmetricity, convergence free, monotonicity and sequence algebra. Further we obtain some relation between these spaces as well as prove some inclusion results.

Keywords: difference sequence, 2-norm, Orlicz function, paranorm, completeness, solidity, symmetricity, convergence free, monotone space.

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