Hybrid algorithm for common fixed points of uniformly closed countable families of hemirelatively nonexpansive mappings and applications (Q410957)

Summary: The authors present in this paper {\parindent=8mm\begin{itemize}\item[(1)] the definition of a uniformly closed countable family of nonlinear mappings, \item[(2)] a strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with a new method of proof, \item[(3)] two examples of uniformly closed countable families of nonlinear mappings and applications, \item[(4)] an example of a hemirelatively nonexpansive, but not weak relatively nonexpansive mapping, and \item[(5)] an example of a weak relatively nonexpansive, but not relatively nonexpansive mapping. \end{itemize}} These results improve and extend those of \textit{S. Plubtieng} and \textit{K. Ungchittrakool} [Nonlinear Anal., Theory Methods Appl., Ser.~A, Theory Methods 72, No.~6, 2896--2908 (2010; Zbl 1203.47070)] and many others.