Modified semi-implicit midpoint rule for nonexpansive mappings
نویسندگان
چکیده
where h > is a stepsize. It is known that if f :RN →RN is Lipschitz continuous and sufficiently smooth, then the sequence {xn} generated by (.) converges to the exact solution of (.) as h→ uniformly over t ∈ [, t̄] for any fixed t̄ > . If we write the function f in the form f (t) = g(t) – t, then differential equation (.) becomes x′ = g(t)– t. Then the equilibrium problem associated with the differential equation is the fixed point problem t = g(t). Based on the above fact, Alghamdi et al. [] presented the following semi-implicit midpoint rule for nonexpansive mappings:
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