Generalized difference operator and topological properties

We divided this thesis into the four chapters. The first chapter of the thesis gives the introduction deals with a historical review. The second and the third chapters give the background of different kinds of work done by various authors, which are related directly to our definitions and results. Most of concepts which we have used throughout the thesis such as notations and definitions are currently standard. We presented the history of the Orlicz function in the the fourth chapter. We used the Peralta' s (2010) studies and extented it by using difference operator ∆_q^m given by Karakaş et al. (2016), we generated the difference sequence space l_p (∆_q^m) and investigated some of their properties. We showed that, if l_p (∆_q^m) is supplied with an aproper norm ‖∙‖_(p,∆_q^m ) then it will be a Banach space. We further more showed that, the sequence spaces (l_p (∆_q^m ),‖∙‖_(p,∆_q^m ) ) and (l_p,‖∙‖_p ) are linearly isometric. At the end of this chapter, it was shown that l_p (∆_q^m)⊂l_p (〖M,∆〗_q^m).