On quasilinear operators between quasilinear spaces

In this work, which consists of five chapter, our main object is to develop the theory of quasilinear operations and quasilinear counterparts of some important theorems and corollaries with respect to linear operations have been stated. In the first chapter, some properties related to families of set-valued function have been presented and important examples have been given for this families. In the second chapter, the basic definitions and theorems which will be useful in the next chapters have been introduced. Also, the family of compact and convex subsets of Rn has been mentioned. In the third chapter, after the introduction of quasilinear spaces and quasilinear subspaces, normed quasilinear spaces have been considered. In the fourth chapter, the concept of quasilinear depandence-independence have been introduced, the notions of bases and dimension have been stated. Furthermore, proper quasilinear spaces have been introduced. In the fifth and final chapter, quasilinear operators and new corollaries with respect to these operations have been presented. In addition, quasilinear operations optained by the way of both real matrix and interval matrix have been discussed.