Generalized vector valued sequence spaces defined by Orlicz function

In the first part of this study consisting of five sections, information is given about the historical development of scalar and vector valued sequence spaces defined by the Orlicz function. In the second chapter, some topological concepts, some inequalities and notions related to the Orlicz function are mentioned. In the first part of the third chapter, we talk about the scalar valued ℓ_{M} Orlicz sequence space, which was introduced by W. Orlicz and later studied by mathematicians such as K. J. Lindberg, J. Lindenstrauss, L. Tzafriri, P. K. Kamthan, M. Gupta, and in the second part, Orlicz sequence spaces ℓ_{M}(p) generalized by S. D. Parashar & B. Choudhary using a bounded sequence (p_{k}) of positive real numbers and some properties of these spaces are mentioned. In the first part of the fourth chapter, we focus on the vector-valued sequence space F(E_{k},M), defined by D. Ghosh & P. D. Srivastava and some of its properties are examined, and in the second part, the vector-valued sequence space F(E_{k},q_{k},M,p_{k},s), defined by M. K. Ozdemir & I. Solak and some of its properties were examined, was included. In the last chapter, the properties of the vector-valued sequence space X(E,Δ^{m},M,p,s) defined by P. D. Srivastava & S. Kumar were examined.