The statement is

"Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they are".

According to one source, Don Koks (a physicist text book author)this statement is true..... on the condition A orbits B.

http://math.ucr.edu/home/baez/physics/Relativity/SR/movingClocks.html

Let A very closely orbit B. The orbit is so close that A is almost touching B; therefore time delays in signal exchanges can be neglected. The faster A orbits B, the FASTER B's clock runs in A's view. Conversely, the SLOWER A's clock runs in B's view.

The motion may be uniform or accelerated; it makes no difference to the principle.

The statement is

"Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they are".

According to one source, Don Koks (a physicist text book author)this statement is true..... on the condition A orbits B.

http://math.ucr.edu/home/baez/physics/Relativity/SR/movingClocks.html

Let A very closely orbit B. The orbit is so close that A is almost touching B; therefore time delays in signal exchanges can be neglected. The faster A orbits B, the FASTER B's clock runs in A's view. Conversely, the SLOWER A's clock runs in B's view.