Cesàro Summable Sequence Spaces over the Non-Newtonian Complex Field

Abstract EN

The spaces ω 0 p , ω p , and ω ∞ p can be considered the sets of all sequences that are strongly summable to zero, strongly summable, and bounded, by the Cesàro method of order 1 with index p .

Here we define the sets of sequences which are related to strong Cesàro summability over the non-Newtonian complex field by using two generator functions.

Also we determine the β -duals of the new spaces and characterize matrix transformations on them into the sets of ⁎ -bounded, ⁎ -convergent, and ⁎ -null sequences of non-Newtonian complex numbers.