In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. 2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L τ spaces; our result generalizes a recent result of Domínguez-Benavides et al. 2009 .
a b s t r a c tIn this paper, we introduce a one-step iterative process to approximate common fixed points of a finite family of generalized nonexpansive multivalued mappings and prove some weak and strong convergence theorems for such mappings in uniformly convex Banach spaces.
Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.
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