On Sequence Spaces of Non-Absolute Type Generated by the Fractional Order Generalized Difference Matrix

Vol. 4  Issue 2
Year: 2015
Issue:Apr-Jun
Title:On Sequence Spaces of Non-Absolute Type Generated by the Fractional Order Generalized Difference Matrix
Author Name:Sinan Ercan and Çigdem A. Bektas
Synopsis:
The difference operator of fractional order and its applications is studied by P. Baliarsingh in [8], introduced the new sequence spaces using difference operator of fractional order in [9] and examined some topological properties of these sequence spaces and also computed their dual spaces. In this paper, using the definition of difference operator of fractional order and using definitions which are given in [6] by M. Mursaleen and A. K. Noman, the authors introduced the sequence spaces c0(Δλ(α)) and c (Δλ(α) ) which are BK-spaces of non-absolute type. The authors also proved that c0(Δλ(α)) and c(Δλ(α)) spaces are linearly isomorphic to the classical sequence spaces c0 and c, respectively. Lastly, we determine the Schauder basis of the c(Δλ(α)),c0(Δλ(α)) and we compute the α-, β- and γ- duals of these spaces.