Stability Of Two Classes Of New Functional Equations

With the development of science and technology,functional equations are involved in research in many scientific fields,such as mechanics,physics,biomathematics,economics,automation,and communication theory.These equations can accurately describe the objective world.Therefore,the study of functional equations has important theoretical value and practical significance.Since the introduction of the viewpoint of functional analysis into equations,both for general and more specific functional equations,rapid development has been achieved,with important results in many aspects such as the basic theory of solutions,the stability theory of solutions,and the operator theory of solutions.Fixed point theory has been extensively studied in Banach spaces and applied to prove the stability of functional equations.The two new functional equations given in this paper are extensions of Cauchy functional equations.Using the fixed point method,the stability problems of these two functional equations are studied,and they are extended to Banach algebras.This thesis is divided into four chapters.In chapter 1,we mainly introduce the background knowledge about the stability of functional equations,and give some preliminary knowledge.In chapter 2,in the complex Banach algebras,we use the fixed point method to study the Hyers-Ulam stability of a new class of additive functional equations,and use it to study the partial multipliers related to the additive functional equations in the Banach *-algebras.In chapter 3,in real Banach algebras,we use the fixed point method to study the HyersUlam stability of another new class of additive functional equations,which generalizes the relevant conclusions in the literature.In chapter 4,make a summary and propose questions that can be further studied in the future.