Looking on the internet deeply has found these results:

within the perspective is the most popular phrase on the web.

in the perspective 137,700,000 results on the web	within the perspective 139,100,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
to say nothing else This subject has not been discussed in the perspective outlined by you, Mr Rübig. I shall stress two of them: the first concerns the guidelines for social policy that are well short of Europe's needs for jobs, welfare and rights in the perspective of Lisbon. I believe the Member States must look at these recommendations in the perspective of gradually approaching our aim. This is important in the perspective of an enlarged Community that will soon comprise 25 Member States and that will certainly benefit from homogenous and directly applicable rules throughout its territory. A valuation undertaken in this context is a favourable factor for the private investor, as it tends to strengthen the prospects of a capital gain in the perspective of valuation multiples returning to their average historical levels. An evaluation of the effectiveness of these principles in the perspective of technological changes is extremely useful.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

in the perspective

137,700,000 results on the web

within the perspective

139,100,000 results on the web

More popular!

to say nothing else
This subject has not been discussed in the perspective outlined by you, Mr Rübig.
I shall stress two of them: the first concerns the guidelines for social policy that
are well short of Europe's needs for jobs, welfare and rights in the perspective of Lisbon.
I believe the Member States must look at these recommendations in the perspective of gradually approaching our aim.
This is important in the perspective of an enlarged Community that will soon comprise 25 Member States and that will certainly benefit from homogenous and directly applicable rules throughout its territory.
A valuation undertaken in this context is a favourable factor for the private investor, as it tends to strengthen the prospects of a capital gain in the perspective of valuation multiples returning to their average historical levels.
An evaluation of the effectiveness of these principles in the perspective of technological changes is extremely useful.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.