Some Euler difference sequence spaces of non-absolute type of order M.

EULER DIFFERENCE SEQUENCE SPACES OF NON-ABSOLUTE TYPE OF ORDER M SUMMARY Keywords: Sequence Spaces Of Non-Absolute Type, Difference Sequence Spaces, Schauder Bases, a -, fi - and y -Duals, Matrix Transformations. This thesis consist of six chapters. In the first chapter, some fundamental definitions and theorems which will be used in the later chapters are given. The sets e£ \Am ), erc [Am J, and e\ \Am J which are the non-absolute type Euler sequences of order m are defined. These sequences spaces are shown to be BK-spaces. Further, inclusion relations among these spaces are also studied. In the second chapter, the Schauder basis of the sequences spaces erc[Am J and erQ \Am ) are computed. In the third chapter, a-,fi-, and y- duals of the sequence spaces <(Am), <(Am),and e0r(A") are computed. In the fourth chapter, the matrix transformation of ( erc[AmJ:lp ), ( erc\Am) :c), and ( erc\Am)\l!0 ) are characterized. Finally, in the fifth and sixth chapters, the results obtained are given and some suggestions for further research are made. VI