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Weak and strong convergence theorems without some widely used conditions. (English) Zbl 1210.47095

Authors’ abstract: We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or FrĂ©chet differentiable norm.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
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