Generalized Difference Lacunary Weak Convergence of Sequences

In this paper, we introduce the concept of generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. We gave appropriate examples and detailed discussions to validate our established  failure instances and definitions. Further, we have established some inclusion relations of the introduced sequence spaces with other sequence spaces, in particularly with the weak Ces`aro summable sequences.

Keywords:

Lacunary sequence , Weak convergence , Ces`aro summable sequence , Banach space , Solid space , Symmetric space