On some set-valued function spaces and analysis of operators between those spaces

This thesis consists of five chapters. In the introduction, some notions relatedto sets and families of set-valued function have been presented.In the second chapter, the basic definitions, concepts, theorems and exampleswhich will be useful in the next chapters have been given.In the third chapter, the family of compact and convex subsets of Rn has beenmentioned. Also, definitions of Hukuhara difference of subsets of Rn, the Hausdorffmetric and continuity of set-valued functions have been introduced.In the fourth chapter, firstly, the concept of semilinear space is considered andsecondly, semilinear structure on sets and families of set-valued function has beenanalyzed. Further, some important properties of them have been presented.In the fifth and final chapter, after the introduction of quasilinear spaces, normedquasilinear spaces and bounded quasilinear operators have been considered. Further,quasilinear counterparts of some important theorems in linear functional analysishave been stated.