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Let  Open image in new window  be a nonempty compact convex subset of a uniformly convex Banach space  Open image in new window , and let  Open image in new window  and  Open image in new window  be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that  Open image in new window  and  Open image in new window  for all  Open image in new window . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary  Open image in new window  by  Open image in new window ,  Open image in new window , where  Open image in new window  and  Open image in new window ,  Open image in new window  are sequences of positive numbers satisfying  Open image in new window ,  Open image in new window , converges strongly to a common fixed point of  Open image in new window  and  Open image in new window ; that is, there exists  Open image in new window  such that  Open image in new window .

Ishikawa Iterative Process for a Pair of Single-valued and Multivalued Nonexpansive Mappings in Banach Spaces