Sentence examples for prove that the generated from inspiring English sources

3, we present the modified proximal gradient algorithm with perturbations and prove that the generated sequence ({x_{n}}) converges strongly to a solution of problem (1).

We prove that the generated sequences converge strongly to theunique solutions of particular variational inequality problems defined over the setof common fixed points of a sequence of nearly nonexpansive mappings.

We proved that the generated iterative sequence converges strongly to a solution of a non-smooth composite optimization problem.

We also proved that the generated hollow void and mesporous lay in carbon spheres could boost dielectric loss ability and impedance match behavior.

This behavior is consistent with the fast destruction of phenol and proves that the generated oxidation products can further react with OH· to form various breakdown products and eventually mineralize.

Supposing that the direction of R c is perpendicular to that of P1, i.e., (varvec{s}_{c}^{text{T}} varvec{s}_{1} = 0), it can be proved that the generated finite screw will not be changed if we use one R c to replace P2, or two R c to replace P1 and P2.

Under suitable conditions, we prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split variational inclusion problem.

Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converges strongly to a solution of the general split equality fixed point problem and the general split equality problem for quasi-nonexpansive mappings in Hilbert spaces.

Moreover, we prove that the operator generated by problem (1.1) is positive.

Next we prove that the sequence generated by (1.14) is well defined and for all.

We first prove that the sequence generated by (1.15) is well-defined.