Some new results of M-iteration process in hyperbolic spaces

Mathematics

In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition (E) in hyperbolic spaces. We consider new concepts of weak w2-stability and data dependence results involving two multivalued almost contractive mappings. We provide examples of multivalued almost contractive mappings to show the advantage of our new iterative algorithm over some exiting iterative algorithms. Moreover, we prove several strong Δ-convergence theorems of our new algorithm in hyperbolic spaces. Furthermore, with another novel example, we carry out a numerical experiment to compare the efficiency and applicability of a new iterative algorithm with several leading iterative algorithms. The results in this article extend and improve several existing results from the setting of linear and CAT(0) spaces to hyperbolic spaces. Our main results also extend several existing res...

International Journal of Mathematics and Mathematical Sciences, 2020

In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.

Mathematical Sciences, 2016

In this paper, we establish strong and D-convergence theorems for a relatively new iteration process generated by generalized nonexpansive mappings in uniformly convex hyperbolic spaces. The theorems presented in this paper generalizes corresponding theorems for uniformly convex normed spaces of Kadioglu and Yildirim (Approximating fixed points of nonexpansive mappings by faster iteration process, arXiv:1402.6530v1 [math.FA], 2014) and CAT(0)-spaces of Abbas et al. (J Inequal Appl 2014:212, 2014) and many others in this direction.

Filomat, 2016

In this paper we prove the strong and 4-convergence theorems of an iteration process of Khan et al. (J. Appl. Math. Comput. 35 (2011) 607-616) for three finite families of total asymptotically nonexpansive nonself mappings in a hyperbolic space. Moreover we obtain the data dependence result of this iteration for contractive-like mappings under some suitable conditions. Also we present some examples to support the results proved herein. Our results extend and improve some recent results announced in the current literature.

International Journal of Mathematics and Mathematical Sciences, 2015

We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several well-known results in Banach spaces as well as CAT(0) spaces.

Symmetry, 2023

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak w 2 -stability and data dependence results for contraction mappings. We also prove some ∆-convergence and strong convergence theorems for generalized (α, β)-nonexpansive type 1 mappings. Finally, we offer a numerical example of generalized (α, β)-nonexpansive type 1 mappings and show that the KF-iteration process is more effective than some other iterations. Our results generalize and improve several relevant results in the literature.

Journal of Applied Mathematics and Physics, 2014

We introduce a general iterative method for a finite family of generalized asymptotically quasinonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.

Thai Journal of Mathematics, 2019

The purpose of this paper is to establish $\Delta$-convergence and strong convergence theorems for the mixed Agarwal-O'Regan-Sahu type iterative scheme \cite{3} to approximate a common fixed point for two generalized nonexpansive multivalued mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results in the literature.

The Korean Journal of Mathematics, 2019

In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give non-trivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.

Journal of Applied Mathematics, 2013

The purpose of this paper is to introduce the concept oftotal asymptotically nonexpansive mappingsand to prove someΔ-convergence theorems of the iteration process for this kind of mappings in the setting ofhyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.