Sentence examples for problems are established from inspiring English sources

Strong convergence theorems for common solutions of the problems are established in infinite dimension Hilbert spaces.

The relationships between the variational-like inequalities and the nondifferentiable pseudoinvex optimization problems are established.

Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established.

A posteriori error estimates of finite-element solutions for those problems are established in Section 3.

Strong convergence theorems for common solutions of two problems are established in the framework of Hilbert spaces.

In this paper, existence, localization and uniqueness results of solutions to elliptic Dirichlet boundary value problems are established.

The uniform separability of these problems is established.

Therefore, a novel algorithm different from Zhang (2003) for this class problems is established.

A strong convergence theorem for solutions of the equilibrium problems is established in a nonuniformly smooth Banach space.

The absence of shear and membrane locking problems is established through the analysis of ultra thin shells.

Later, optimality and duality results for PDI&PDE-constrained optimization problems were established by Pitea et al. in [14] and [15].