Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 631-647

Title CONVERGENCE THEOREMS OF A MODIFIED ITERATION PROCESS FOR GENERALIZED NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES

Author Preeyalak Chuadchawna, Ali Farajzadeh and Anchalee Kaewcharoen

(Received May 20, 2019, revised September 19, 2019)
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 [10]. Our results are the extension and improvement of the results in Ritika and Khan [10]. Moreover, in the numerical example we also illustrate an example for supporting our main result.

Mathematics Subject Classification. Primary 47H10; Seconday 54H25.
Key words and phrases. $\Delta$-convergence theorems, strong convergence theorems, the condition $(E)$, hyperbolic spaces.

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