A class of vector-valued sequence spaces is introduced employing the fractional difference operator $\Delta^{(\alpha)}$, a sequence of modulus functions and a non-negative infinite matrix. Sequence spaces of this class generalize many sequence spaces which are defined by difference operators and modulus functions. It is proved that the spaces of this class are complete paranormed spaces under certain conditions. Some properties of these spaces are studied and it is shown that the spaces are not solid in general.
Srivastava, P., & Mahto, S. (2017). A Class of Sequence Spaces Defined by Fractional Difference Operator and Modulus Function. Khayyam Journal of Mathematics, 3(2), 134-146. doi: 10.22034/kjm.2017.49370
MLA
Parmeshwary Dayal Srivastava; Sanjay Kumar Mahto. "A Class of Sequence Spaces Defined by Fractional Difference Operator and Modulus Function". Khayyam Journal of Mathematics, 3, 2, 2017, 134-146. doi: 10.22034/kjm.2017.49370
HARVARD
Srivastava, P., Mahto, S. (2017). 'A Class of Sequence Spaces Defined by Fractional Difference Operator and Modulus Function', Khayyam Journal of Mathematics, 3(2), pp. 134-146. doi: 10.22034/kjm.2017.49370
VANCOUVER
Srivastava, P., Mahto, S. A Class of Sequence Spaces Defined by Fractional Difference Operator and Modulus Function. Khayyam Journal of Mathematics, 2017; 3(2): 134-146. doi: 10.22034/kjm.2017.49370