Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature.

THE EXISTENCE OF A SOLUTION OF THE NONLINEAR INTEGRAL EQUATION VIA THE FIXED POINT APPROACH

In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework of uniformly convex hyperbolic space and also propose a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex hyperbolic spaces. Furthermore, we establish some basic properties and some strong and $\triangle$-convergence theorems for these mappings in uniformly convex hyperbolic spaces. Finally, we present an application to the nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper extends and generalizes corresponding results in uniformly convex Banach spaces, CAT(0) spaces and other related results in literature.

Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces

We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ -convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT( κ ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces

In this paper, we establish some strong and 4-convergence theorems of an iteration process for approximating a common fixed point of three nonexpansive mappings in a uniformly convex hyperbolic space. The results presented here extend and improve various results in the existing literature.

Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.