The Hyers-Ulam Stability Of Jensen Type Equations

Master thesis "The Hyers-Ulam Stability of Jensen Type Equations" discussesthe Hyers-Ulam stability property of Jensen equation 2f((x+y)/2)-f(x)-f(y)=θ,(1.1)and the Hyers-Ulam stability property of a five-variate Jensen type equation 5f((x+y+z+w+v)/5)+3f((x+y+z)/3)+3f((y+z+w)/3)+3f((z+w+v)/3)+3f((w+v+x)/3)+3f((v+x+y)/3)-4f((x+y+z+w)/4)-4f((y+z+w+v)/4)-4f((z+w+v+x)/4)-4f((w+v+x+y)/3)-4f((v+x+y+z)/4)=θ. (1.2)inβ-homogeneous F~*-spaces. There are four chapters in the paper. Chapter 1mainly introduces above Jensen equation and Jensen type equation and the back-ground of their stability property. In chapter 2, we introduce the conception of F~*-spaces and some theories and notations needed in the following chapters. Chapter 3and chapter 4 is the main works of this paper, we mainly study the the Hyers-Ulamstability of (1.1) and (1.2) in F~*-space with certain property. In chapter 3, we com-pute the stability property of (1.1) inβ-homogeneous F~*-spaces if parameter p, qsatisfy certain condition. In chapter 4, we obtain the stability property of (1.2) inβ-homogeneous F~*-spaces on some certain real number intervals.