Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

Abstract:
We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for continuous monotone mappings.
Language:
English
Published:
Bulletin of Iranian Mathematical Society, Volume:38 Issue: 4, 2012
Page:
1047
https://www.magiran.com/p1112094