We introduce the notion of a C * -algebra-valued b-metric space. We generalize the Banach contraction principle in this new setting. As an application of our result, we establish an existence result for an integral equation in a C * -algebra-valued b-metric space.

We present the extension of Caristi's fixed point theorem for mappings defined on C * -algebra valued metric spaces. We prove the existence of fixed point using the concept of minimal element in C * -algebra valued metric space by introducing the notion of partial order on X.

We compare the rate of convergence for some iteration methods for contractions. We conclude that the coefficients involved in these methods have an important role to play in determining the speed of the convergence. By using Matlab software, we provide numerical examples to illustrate the results. Also, we compare mathematical and computer-calculating insights in the examples to explain the reason of the existence of the old difference between the points of view. MSC: 47H09; 47H10

In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.

We provide a new two-step iteration scheme of mixed type for two asymptotically nonexpansive self mappings in the intermediate sense and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong and weak convergence theorems for mentioned scheme and mappings in uniformly convex Banach spaces. Our results extend and generalize the corresponding results of Chidume et al. [