Published in
Journal of Nonlinear Sciences and Applications, 06(08), p. 997-1004
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On certain Euler difference sequence spaces of fractional order and related dual properties
Journal article published in 2015 by
Ugur Kadak 
,
P. Baliarsingh
,
P. Baliarsingh
Abstract
The purpose of this paper is to generalize the Euler sequences of nonabsolute type by introducing a generalized Euler mean difference operator $E^r(Δ^{(\tilde{\alpha})})$ of order $α$. We investigate their topological structures as well as some interesting results concerning the operator $E^r(Δ^{(\tilde{\alpha})})$ for a proper fraction $\tilde{\alpha}$. Also we obtain the $α$-,$β$- and $γ$-duals of these sets.