Perturbations And Approximations Of C-regularized Resolvent Families

In this paper ,some basic properties of C-regularized resolvent families have been studiedincluding Additional Perturbations, Pseu- C1-resolvent , Convergence and Approximation of C-Regularized resolvent families.This article contains five parts .The first chapter introduces the history and development of C-Regularized resolvent families brie?y. Perturbations is an important property of resolvent families.In the second chapter, we study additive perturbation of C-Regularized resolvent families.Supposed that closed linear operator A generates a C-regularized resolvent family , these's aoperator CB to make operator A+B also generates a new resolvent family.In the third chapter, we discuss the condition when a pseu-C1 resolvent family becomes a C1-resolvent,i.e. it is equivalent with ker(?(λ)) = 0and R(?(λ)) which is dense in X that pseu- C1regularized resolvent {?(λ) :λ∈} becomes a C1 Resolvent L(λ: A) which is generated bydense domains closed linear operator A . This result is to prepare for studying Convergence andApproximation of C-Regularized resolvent family in next chapter.The forth chapter mainly studies that Convergence of resolvent generated by A is equivalentwith Convergence of C-Regularized Resolvent Families. Moreover, the convergence is uniform int on every compact subject of R+.The last chapter is about concept, definition and generation theory of k-convolve C-semigroup .we will study such additional Perturbations, Convergence and Approximation andUniform Continuity as C-Regularized resolvent families.