Approximating the solution of a nonlinear delay integral equation by an efficient iterative algorithm in hyperbolic spaces

Abstract

In this article, we propose the modified AH iteration process in Hyperbolic spaces to approximate the fixed points of mappings enriched with condition $ (E) $. The data dependence result of the proposed iteration process is studied for almost contraction mappings. Further, we obtain several new strong and $ \vartriangle $-convergence results of the proposed iteration algorithm for the class of mappings enriched with the condition $ (E) $. Also, we illustrate the efficiency of our results over existing results in literature with the aid of some numerical examples. Finally, we use our main results to find the solution of nonlinear integral equation with two delays.

Keywords

• hyperbolic space
• data dependence
• strong and $ \vartriangle $-convegence
• almost contraction mapping
• mappings satisfying condition $ (e) $ and nonlinear integral equation