Sentence examples for method we proved from inspiring English sources

Further, using the hybrid projection method, we proved the strong convergence of the sequences generated by the iterative algorithm.

Throughout this paper, using the fixed point method, we proved the Hyers-Ulam-Rassiasstability of a mixed type ACQ functional equation in fuzzy Banach spaces.

Under suitable assumptions on relaxation functions, damping terms, and source terms, by using the energy method we proved a global nonexistence result for certain solutions with negative initial energy.

Throughout this paper, using the fixed point and direct method we proved the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in non-Archimedean Banach spaces.

Using this single-molecule method, we proved the long-standing hypothesis that neuronal SNAREs assemble by a zippering mechanism and discovered a half-zippered SNARE intermediate that plays a crucial role in the synchronized, calcium-triggered synaptic vesicle fusion (Gao et al., 2012).

Using the contradiction method, we prove the lemma.

Using the Picard iteration method, we prove the existence of equation (1.1) in Sect.

Using the periodic unfolding method, we prove some convergence results and describe the homogenized problems.

Using the fixed-point method, we prove the generalized Hyers-Ulam stability of the functional equation.

Using fixed point method, we prove the Hyers-Ulam stability of derivations on proper Jordan CQ*-algebras.

Using the discrete energy method, we prove the compact difference scheme is unconditionally stable and convergent.