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From Lemma 2.2 that the net generated by converges strongly to, as.

Since is a nonexpansive mapping, we have from [12, Theorem ] that the net generated by converges strongly to, as.

It is proved that the sequence generated iteratively by converges strongly to a common fixed point which solves the variational inequality for all.

It follows from Theorem 3.1 that generated by converges strongly to, as, where is the unique solution of a variational inequality.

Theorem 4.3Under the assumptions of Theorem 4.2, if in additionCis assumed to beρ-compact, then the sequence generated by converges strongly to a common fixed point, that is, (4.21).

It is well known that if is Lipschitzian and strongly monotone, then for small enough, the mapping is a contraction on and so the sequence of Picard iterates, given by converges strongly to the unique solution of the.

By Theorem 3.3, the iterative sequence ({x_{n}}) generated by (4.9) converges strongly to ({x^ = {P_{operatorname{VI}(C,A)}}theta=P_{operatorname{Fix}(T }theta).

If the solution set of problem (22) denoted by Ω is nonempty, then the sequence { x n } generated by (23) converges strongly to P Ω ( 0 ).

Then defined by (2.1) converges strongly to.

Then, generated by (1.14) converges strongly to an element in.

We prove that defined by (1.14) converges strongly to.