Then for any given, the sequence defined by Algorithm 3.6 converges strongly to a solution of GMEPP (2.1).
then the sequence { x n } defined by algorithm (4.2) converges in norm to the unique minimizer of (4.1).
Then for any given, the sequence defined by Algorithm 3.6 converges weakly to a solution of GMEPP (2.1).
where is the same as in Lemma 2.8, for any, the iterative sequences, and defined by Algorithm 3.4 converge strongly to the solution of (2.9).
where is the same as in Lemma 1.13, then, for any, the iterative sequences, and defined by Algorithm 2.6 converge strongly to the solution of the problem (1.4).
then the generalized strongly nonlinear mixed variational-like inequality (2.1) possesses a solution and the sequence defined by Algorithm 3.2 converges to.
Further, -converges to a solution of (4.40) and -converges to, where the sequences in and in are defined by Algorithm 2. Proof.
and one of (4.3)–(4.6), then the generalized strongly nonlinear mixed variational-like inequality (2.1) possesses a solution and the sequence defined by Algorithm 3.2 converges to.
for all, where is the same as in Lemma 2.8, for any, the iterative sequences, and defined by Algorithm 3.3 converge strongly to the solution of (2.8).
When we compare Lemmas 2.1 and 2.2 by Lemmas 4 and 5 in [10], we note that the sequence ({X_{s}}), (s=0,1,2,ldots) (which is defined by Algorithm 2.1) satisfies the same properties of the sequence ({X_{s}}), (s=0,1,2,ldots ) (which is defined by Algorithm (2.2) in [10]).
