The Isometric Extension Of The Unit Spheres Of C₀ And The Ulam Stability Of A Seven Variable Jensen Type Equation

There are three chapters in the paper.Chapter 1 mainly introduces some basic results about the paper, including someconceptions and notations needed in the following chapters.In chapter 2, we study the isometric extension of the into mapping between theunit spheres of Co. we obtain some sufficient conditions under which an isometricembedding between unit spheres of Co can be really linearly isometrically extendedto the whole space.In chapter 3, we mainly investigate the Hyers-Ulam stability of a 7-variateJensen type functional equation, getting the corresponding error formulas in whichtheβ-homogeneity of the F-norm is closely associated with the approximate re-mainderφ. Furthermore, we make sure p_i's area in which the Hyers-Ulam-Rassiasstability is affirmative or negative where P_i for i = 1, 2,…, 7 can be different.