On the Euler sequence spaces which include the spaces ℓp and ℓ∞ I☆

Altay, Bilâl; Başar, Feyzı; Mursaleen, M.

doi:10.1016/j.ins.2005.05.008

Cited by 163 publications

(106 citation statements)

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“…The results presented in this article not only generalize the earlier works done by several authors [2,3,4,21] but also give a new perspective concerning the development of the Euler spaces of difference sequences. As future work we will study certain matrix transformations of Euler spaces of fractional order and Riesz mean difference sequence of fractional order.…”

Section: Resultssupporting

confidence: 84%

On certain Euler difference sequence spaces of fractional order and related dual properties

Kadak¹,

Baliarsingh²

2015

J. Nonlinear Sci. Appl.

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The purpose of this paper is to generalize the Euler sequences of nonabsolute type by introducing a generalized Euler mean difference operator E r (∆ (α) ) of order α. We investigate their topological structures as well as some interesting results concerning the operator E r (∆ (α) ) for a proper fractionα. Also we obtain the α-, β-and γ-duals of these sets.Keywords: Euler sequence spaces of nonabsolute type, linear operator, matrix transformations, α-, β-and γ-duals. 2010 MSC: 46A45, 46A35, 46B45.

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