Sentence examples for methods converge strongly from inspiring English sources

We then prove that the proposed iterative methods converge strongly to the minimum-norm solution of the variational inequality.

Furthermore, we prove that the proposed viscosity iteration methods converge strongly to a particular solution of the mixed equilibrium problem (1.3) and the split feasibility problem (1.1).

We first propose implicit and explicit iterative schemes for solving a constrained convex minimization problem and prove that the methods converge strongly to a solution of the minimization problem, which is also a solution of the variational inequality.

It is proved that the proposed method converges strongly to a common solution of above problems under some assumptions.

Furthermore, we prove that the proposed iterative method converges strongly to a common element of the above three sets, and we also apply our results to complementarity problems.

It is proved that under appropriate conditions, the sequence generated by the hybrid shrinking projection method converges strongly to some point in (mathit{EP} cap F).

He proved that the sequence generated by the proposed method converges strongly to the unique solution of the quadratic minimization problem.

It is shown that the net defined by the suggested implicit extragradient method converges strongly to the unique solution of in Hilbert spaces.

It is shown that the net defined by this implicit extragradient method converges strongly to the unique solution of in Hilbert spaces.

Marino et al. [27] introduced a multi-step iterative method that generalizes the two-step method studied in [19] from two nonexpansive mappings to a finite family of nonexpansive mappings, and proved that the sequence generated by this method converges strongly to a common fixed point of the mappings which is also a solution of the equilibrium problem (1.6).

By combining the iterative schemes proposed by Moudafi [1] and Xu [4], Marino and Xu [6] considered a general iterative method and proved that the sequence generated by the method converges strongly to a unique solution of a certain variational inequality problem, which is the optimality condition for a particular minimization problem.