Do you mean influence of style or influence of subject?
Every author really has his a style and when it comes to style we (not authors, I mean humans in general) all influence each other. It would be unfair to point a finger at an author for using the same figure of speech as another one.
But Nietzsche was vocal enough about Dostoevsky's influence on him. There was no shame associated. You know Nietzsche had a bit of a personality and did like himself quite a bit and yet he said that Dostoevsky was the only psychologist he had anything to learn from. I believe Nietzsche read Dostoevsky for the first time in 1887. I am not sure though. I don't remember what book it was that he read first either.
It is said the Nietzsche had a deep inner dialogue with Dostoevsky until the last moment of his life (or his sanity). But of course, their worldviews deeply diverged, and that is why it is so very difficult to connect them. Their relationship is a field of study in both philosophy and literature. Nietzsche's concept of übermensch (my people fought against the Nazi, so that word always makes me shiver a bit - though it is nothing but a misunderstood philosophical concept) is supposedly derived from Dostoevsky's Raskolnikov (Crime and Punishment), Kirillov (The Possessed) and Ivan Karamazov (Karamazov), for example.
Now, obviously, I am no philosopher or PhD in literature but there are so many interesting papers about their relationship. And it is fascinating to see how Russian critics maintained that Nietzsche and Dostoevsky were in irreconcilable opposition with each other. And yet …
As for Kafka, he owned almost all of Dostoevsky's works. Critics consider that Kakfka used parts of "The Double" by Dostoevsky to write "The Metamorphosis" (what a magnificent short story, don't you agree?!). It is quite accepted, since the 50s, that it is so.
Of course, this hurts our contemporary perception of originality and copyrights. But when one thinks about it, is it so very wrong to sit on the shoulders of giants? And aren't we wrong to believe ideas are our properties? It wasn't like that back then. They admired Dostoevsky, Dostoevsky influenced them. They might have diverged from him or continued on his tracks, but they did not just flush the past and tried to rebuild literature from scratch. They moved on and built upon what was readily available.
Something we have stopped to do, believing we are superior enough to write without reading the works of others. And thus, producing so much mediocrity. Yes, I am a literary pessimist.
I am sorry for this, for drowning you in my obsessions. People around me don't really care about the birth of psychological literature. Nietzsche is read by men who butcher the concept of stoicism, nowadays. Kafka is obscure and unknown. And Dostoevsky is only remembered as the evil Russian supremacist who got critiqued by Nabokov (all hail Nabokov ). Urgh.