Some of my advanced original problems
© Copyright: Cristinel Mortici

A11. Let  and  be a sequence of real numbers such that for every

Prove that

A10. For every real number  define  by the relation

Prove that  is a well defined integrable function, then compute

A9. Let there be given   and the inequality

Prove that:

(i) If  holds whenever  then

(ii) If  holds whenever  then

A8. Find  with the intermediate value property such that

A7. Solve in real numbers:

A6. Find all derivable functions  such that

A5. Let  be linear on each interval  such that  for every integer  with  Prove that  is antiderivable.

A4. Let  be  matrices with real entries such that  Prove that

A3. Let  be  matrices with complex entries such that  Prove that  or

A2. Let  be elements of a ring ,  inversable, such that

whenever  Prove that

A1. Let  be continuous such that for every reals , there exist , with  such that

Prove that  is nondecreasing.