Consider two applications: one (num. 1) that invokes malloc() many times, and the other (num. 2) that invokes malloc() few times. Both applications allocate the same
You don't define the relative difference between "many" and "few" but I suspect most mallocs would function almost identically in both scenarios. The question implies that each call to malloc has as much overhead as a system call and page table updates. When you do a malloc call, e.g. malloc(14), in a non-brain-dead environment, malloc will actually allocate more memory than you ask for, often a multiple of the system MMU page size. You get your 14 bytes and malloc keeps track of the newly allocated area so that later calls can just return a chunk of the already allocated memory, until more memory needs to be requested from the OS.
In other words, if I call malloc(14) 100 times or malloc(1400) once, the overhead will be about the same. I'll just have to manage the bigger allocated memory chunk myself.