Convergence theorems of a modified iteration process for generalized nonexpansive mappings in hyperbolic spaces

Abstract

In this paper, we introduce a modified Picard-Mann hybrid iterative process for a finite family of mappings in the framework of hyperbolic spaces. Furthermore, we establish $\Delta$-convergence and strong convergence results for a sequence generated by a modified Picard-Mann hybrid iterative process involving mappings satisfying the condition $(E)$ in the setting of hyperbolic spaces which more general than one mapping in the setting of CAT(0) spaces in Ritika and Khan [19]. Our results are the extension and improvement of the results in Ritika and Khan [19]. Moreover, in the numerical example we also illustrate an example for supporting our main result.