Some new sequence spaces defined by Orlicz function

In the first chapter of this work, certain attributes of N-functions and Orlicz functions which are taken part in the special classes of convex functions and studied in detail by M.A. Krasnosel'skii & Y.B. Rutickii and later M.M. Rao & Z.D. Ren, are introduced. In the second chapter, previously, Orlicz sequence space £m which is a directly generalization of £p space was introduced. Also, some usual problems of functional analysis as completeness, separability conditions and equivalent normizations are considered for this space. Then, the sequence space £m{p) which is developed by S.D. Parashar & B. Choudhary with any bounded sequence of positive real numbers (pk), is studied. In the last chapter, vector valued Orlicz sequence spaces are presented. Firstly, a generalizations of £m developed by D. Ghosh & P.D. Srivastava is considered. Secondly, we defined an Orlicz sequence space which is a generalization of lu in many respect and investigated some properties of this sequence space. KEY WORDS: Orlicz sequence space, Orlicz function, N-function, paranormed space, vector valued sequence space n