On the New Hahn Sequence Space h(2) - Orhan Tuğ (Abstract and Applied Analysis)
This paper investigates the properties and structural characteristics of the new Hahn sequence space defined by using the second-order forward difference operator. First, we introduce the new Hahn sequence space:  h2=x=xl∈ω:∑l=1∞l+1 Δ2xl<∞, liml→∞xl=0,of order two. Then, we show some topological properties of this new sequence space h2, and calculate our new Hahn sequence space’s alpha-dual, beta-dual, and gamma-dual. Finally, we calculate some matrix transformations from the new Hahn sequence space  h2 into the space α=l1,l∞, c,c0, lr, h and from the space β=l1,l∞, c,c0, lp, h into the new Hahn sequence space  h2.