Gunduz, Birol; Aydoğdu, Ebru; Aygün, Halis

In this paper, we give a multivalued version of Picard-Mann hybrid iterative process of Khan [4] in Kohlenbach hyperbolic space. This process converges faster than all of Picard, Mann and Ishikawa iterative processes. By using an idea of Shahzad and Zegeye [8] which removes a restriction on the mapping and the method of direct construction of Cauchy sequence as illustrated by Song and Cho [9], we obtain strong and Δ-convergence theorems of this process for a multivalued mapping. Our results improve corresponding results of Shazad and Zegeye [8], Song and Cho [9] and many other in the contemporary literature in terms of faster iteration, more general space and weaker condition on mapping T.

Gunduz, Birol; Karahan, Ibrahim

The present paper aims to deal with multivalued version of SP iterative scheme to approximate a common fixed point of three multivalued nonexpansive mappings in a uniformly convex hyperbolic space and obtain strong and Δ-convergence theorems for the SP process. Our results extend some existing results in the contemporary literature.