Stability Of Functional Equations And Derivations In Fuzzy Banach Space

In 1940,Ulam introduced the basic question of group homomorphic stability,the problem description is about to give an approximate group homomorphism map arbitrarily.Does there exist a group homomorphism map that approximates to it? In 1941,Hyers gave the first affirmative partial answer.Then Rassias weakened the bounded Cauchy difference of Hyers and extended Hyers' s conclusion to the unbounded Cauchy difference.The stability of this kind of equation is called Hyers-Ulam-Rassias stability.In particular,in the past three decades,the notion of stability functional equation has evolved into an area of continuing research from both pure and applied viewpoints.Many scholars have done a lot of researches on functional equation.The development of functional equation research has become more perfect.The functional equation types are diversified,space diversity and application are widely.The stability of the equation is still one of the classical topics in functional equation research.In this paper,the stability of functional equations and derivations are studied,which consists of two parts: the first part proves the stability of pexider inequality in fuzzy Banach spaces by direct method;the second part proves the Hyers-Ulam stability of the n-Jordan ~*-derivations on induced fuzzy C~*-algebras by fixed point method.By comparing the conditions and conclusions of the theorem,it can be concluded that the positions and ranges of coefficients of the equation are different,which have different effects on the stability of the equation.This paper is divided into three chapters.The first chapter,we mainly introduce the research background and development status of functional equation and inequality stability.In the second chapter,we introduce the fuzzy Banach space and its related definitions.In the fuzzy Banach space,we use direct method to prove the stability of two Pexider inequalities,and give relevant inferences.In the third chapter,the induced fuzzy C~*-algebra,~*-derivation and related definitions are introduced.The Hyers-Ulam stability of n-Jordan ~*-derivations is proved by using the fixed point method,and the related inferences are given.