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An Application of Lacunary Summability Method to n-Norm

Hemen Dutta

Abstract


In this article we use the idea of strongly lacunary summability method and n-norm to construct some new type of difference sequence spaces. We study these spaces by defining non-standard n-norm and derived (n-p)-norm for every p =1, . . .,n-1. We show that these spaces become n-Banach spaces when the base space is an n-Banach space or Banach space when the base space is equipped with standard n-norm. We also show that under certain cases convergence and completeness in the n-norm is equivalent to those in the (n-p)-norms. Further we prove the Fixed Point Theorem for these n-Banach spaces.

Keywords


n-normed spaces, Lacunary sequence, completeness, Fixed Point Theorem.

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