Sentence examples for mappings by applying from inspiring English sources

Zhang et al. [20] investigated some minimax problems for set-valued mappings by applying the Fan-Browder Fixed Point Theorem.

Some generalized Ky Fan minimax inequalities for vector-valued mappings are established by applying the classical Browder fixed point theorem and the Kakutani-Fan-Glicksberg fixed point theorem.

Chang et al. [6] obtained a Ky Fan minimax inequality for vector-valued mappings on W-spaces by applying a generalized section theorem and a generalized fixed point theorem.

Further evaluation of this mapping is often accomplished by applying "consistence check" to the set of initial mappings.

The visual quality of the resulting images is evaluated over seven HDR images by applying tone-mapping and computing the PSNR and the HDR-VDP metrics.

Note that the jackstraw disrupts the systematic variation among the randomly chosen s rows by applying independently generated permutation mappings.

Moreover, by applying the continuity of the mappings A, B, g, and J φ to (2.1), we have.

The code architecture facilitates workload balancing among processors for arbitrary mesh refinement depths maintaining intra-level data locality via space-filling curve mappings and, at the same time, ensuring inter-level data locality by applying a novel technique called block sharing.

We defined RF borders as polygons by applying a threshold of 90% of the map peak response value for both local and global mappings (Fig.  2).

By using these generalizations and by applying the order-increasing upward property of set-valued mappings, we prove several existence theorems of the extended and generalized Nash equilibria of nonmonetized noncooperative games on chain-complete preordered sets.

By applying some fixed point theorems in posets and by using the order-preserving property of mappings, we prove an existence theorem of extended Nash equilibriums for nonmonetized noncooperative games.