Fixed Point Theorems And Iterative Sequence Convergence Of Some Mappings

In this paper,first we establish some fixed point theorems for two classes of?-contractive type mappings in complete fuzzy metric spaces,and also discuss the existence and uniqueness of solutions for a class of functional equations arising in dynamic programming by using the fixed point theorem in fuzzy metric spaces.At the same time,we study the existence of fixed points for Ciric-Altman type mappings and nonunique fixed points with symmetric function in orbitally complete metric spaces,and prove the new fixed point theorems.Next,we introduce a finite family asymptotically pseudocontractive type mappings in real normed linear spaces.A strong convergence theorem of iterative scheme with errors for a finite family asymptotically pseudocontractive type mappings in normed linear spaces is established under weaker conditions.Several examples are also given to show the validity and universality of the result presented in this paper.Then,we introduce a new class of generalized asymptotically S-demi-contractive type mappings in real normed linear spaces.Strong convergence theorem of iterative sequences with error associated with a finite family of generalized asymptotically S-demi-contractive type mappings is established.Finall,we study convergence and stability problems of iterative sequences with error for Lipschitz k-subaccretive operators equation x+Tx=f in real Banach space and give a new convergence rate estimate in our results,which extend and improve the corresponding results in some references.