Merhabalar,

I´d really love someone to explain to me the difference between using -mek üzere and -mek için when -mek üzere have -mek için same meaning.

teşekkürler

The - mAk üzere´ gerundium is ;

1. preferred to use for formal and reported statements. And it can mean same as "için" [in order to, to , for ]

Cumhurbaşkanı Atina´ya gitmek üzere THY uçağına bindi. *

The president got on the THY airplane in order to go to Athens.

In the sentence above, - mek üzere is preferred since the statement is formal, it is a news report. 

Cumhurbaşkanı Atina´ya gitmek için THY uçağına bindi. ---> This way is correct too. But it is not as formal as the first sentence.

2.  for the purpose of ….. 

The action is performed for the purpose of a targeted action.

Let´s give an example ;

Türkçe öğrenmek üzere bir kursa yazıldılar.

They enrolled a course in order to [for the purpose] learn Turkish.

The purpose of their enrolling a course was to learn Turkish.

when we use ´için´ for the same sentence, it sounds simplier, more natural and an ordinary act that doesn´t stress the purpose of action as much as ´üzere´ does.

Türkçe öğrenmek için bir kursa yazıldılar.

They enrolled a course to [in order to] learn Turkish.

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3. If the aim [purpose] of an action is simple, unimportant, ordinary, informal  than we just use "için".

Ekmek almak için bakkala gittim.

I went to the shop to get bread.

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4. In stories, authors use ´üzere´ more than we use in daily life.

Keloğlan prensesi görmek üzere saraya gitti.

Keloğlan went to the palace in order to [for the purpose] see the princess.

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5. in negative form it stresses the action will NOT happen again[anymore].

Evi bir daha gelmemek üzere terk etti.

He left home for good.

He left home aiming that he will not come back again.

He left home and he intends NOT to come back again.

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So, If you are still not sure which one to use, than my advice is Don´t take risk and just use ´için´, since ´üzere´ does not suit for all statements.

This is my understanding, may be someone else can explain better.

 ´üzere´  also used as "almost " ,´ about to ´

Vakit bitmek üzere. Biraz çabuk ol.

Time is almost over. Hurry up.

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Kız bugün çok yorgun. Koltukta uyumak üzere.

The girl is very tired today. She is about to sleep on the settee.

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past tense ;

Evden tam çıkmak üzereydim ki komşum geldi.

I was just about to leave home that my neighbour came .

Oh my God! This is so great!

I really appreciate your explanation.

Is there any relation between possibility or doubt to happen in using üzere or için?

Yani for example if I´m sure something is going to happen (...) is preferred to be used, and vice versa?

Çok teşekkür ederim gerçekten.

I don´t think so. There is no sense of   possibility or doubt in using "üzere" or " için" but there is sense of condition , purpose ; mesela ;

Bu parayı geri ödemek üzere alıyorum. ----> I am taking this money in condition that I will pay it back.

İngilizce öğrenmek üzere İngiltere´ye gitti. ---> He went to England in order to [for the purpose] learn English.

Ev almak için para biriktiriyorum. ----> I am saving money in order to [to] buy a house.

* There can also be sense of  agreement, hope in some usages of "üzere" ;

 Aynı yerde bir daha buluşmak üzere ayrıldık.

We left each other agreeing to meet again in the same place.

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Görüşmek üzere ! -----> [hoping to ] See you later ! 

                                       [hoping to ] See each other again !

Nobody could explain better. 

For me, yes...

Example,

Ankaraya gitmek için trene bindim.

Ankaraya gitmek üzere trene bindim.

The difference in meaning of the two sentences above is,

- The first sentence identifies your intention to go to Ankara as your immediate goali. You will get on the train-spend the travelling time- get of in Ankara. There are no intermediate goals in between.

- The second one hints that your intention is to arrive at Ankara eventually, yet there may be several less important intermediate tasks you must attend to before you reach Ankara. There may be more than one stop-overs on the way and your trip may take considerably longer than the first case.

Arguable.

Oh my God!

Both of these posts did the job!

A thousand thanks for both of you!

I really appreciate that