Sentence examples for bounded common solution of from inspiring English sources

So A 1, A 2, J 1, and J 2 have a unique common fixed point h ∗, that is, h ∗ ( x ) is the unique bounded common solution of the functional equations (3.1a) and (3.1b), i = 1, 2. □.

Therefore Corollary 3.3 applies, wherein and correspond, respectively, to the maps and Therefore, and have a unique common fixed point that is, is the unique bounded common solution of the functional equations (4.1) and (4.2).

If every nonempty, bounded, closed, and convex subset of E has the fixed point property for nonexpansive mapping, then ({x_{n}}) converges strongly to a common solution of the equations (A_{i}(x)=0) for (i=1,2,ldots,N).

As a consequence of the presented results, we discuss the existence and uniqueness of the common bounded solution of a functional equation arising in dynamic programming.

Proof Let x be a bounded nonoscillatory solution of (1.1).

Each bounded regular solution of the equation (1.5) is oscillatory.

(4.4). is a bounded positive solution of (1.1).

Therefore, is a bounded nonoscillatory solution of (1.11).

Let w be a bounded positive solution of (48).

Now let w be a bounded positive solution of (48).

Here, w is the unique bounded positive solution of (48 ).