Cesàro summable sequence spaces over the non-Newtonian complex field (Q1658010)

Summary: The spaces \(\omega_0^p\), \(\omega^p\), and \(\omega_{\infty}^p\) 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 \(\beta\)-duals of the new spaces and characterize matrix transformations on them into the sets of \(\ast\)-bounded, \(\ast\)-convergent, and \(\ast\)-null sequences of non-Newtonian complex numbers.