Re: proving a function is continuous

In article <1128009048.774975.45660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Artur <artur_steiner@xxxxxxxxx> wrote:

> Hello
>
> I'd like some hints tro prove that, if I is an interval of R and f:I ->
> R is bounded on I and satisfies f((x+y)/2) <= ((f(x) + f(y))/2 for
> every x and y in I, then f is continuous.
>
> Thank you
>
> Artur
>

If I is a closed interval, such a function may
be discontinuous at the endpoints.

Assuming no endpoints, then your question is *at least* as hard
as the one that says a solution of f(x+y)=f(x)+f(y) that
is bounded on some interval must be continuous.
.