Strong convergence of Mann's type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert spaces

作者：Deng Wei Qi^*

来源：Optimization Letters, 2014, 8(2): 533-542.

DOI：10.1007/s11590-012-0595-0

• Equilibrium problems
• Monotone mappings
• Relatively quasi-nonexpansive mappings
• Strong convergence
• Variational inequality problems

Let be a nonempty closed convex subset of a real Hilbert space . Let be an infinite family of generalized asymptotically nonexpansive nonself mappings. By using a specific way of choosing the indexes of the involved mappings, we prove strong convergence of Mann's type iteration to a common fixed point of without the compactness assumption imposed either on or on provided that the interior of common fixed points is nonempty. The results extend previous results restricted to the situation of at most finite families of such mappings.

• 出版日期2014-2
• 单位云南大学