With one of American Psycho's epigraphs being from "Notes from underground" by Dostoevsky, it's safe to say there's more than a little influence of his work in American Psycho.
Where it really shows is in the chapter End of the 1980s, which specifically references Dostoevsky's "Crime and Punishment."
From Crime and Punishment:
'Man grows used to everything, the scoundrel!'[...]
'And what if I am wrong?' he cried suddenly after a moment's thought. 'What if man is not really a scoundrel - man in general, I mean, the whole race of mankind - then all the rest is prejudice, simply artificial terrors and there are no barriers and it's all as it should be.'
From American Psycho:
“Come on, smile,” she urges sometime later. “You have no reason to be so sad.”“I know,” I sigh, relenting. “But it’s … tough to smile. These days. At least I find it hard to. I’m not used to it, I guess. I don’t know.”
“That’s … why people need each other,” she says gently, trying to make eye contact while spooning the not inexpensive sorbet into her mouth.
“Some don’t.” I clear my throat self-consciously. “Or, well, people compensate.… They adjust.…” After a long pause, “People can get accustomed to anything, right?” I ask. “Habit does things to people.”
… there is an idea of a Patrick Bateman, some kind of abstraction, but there is no real me, only an entity, something illusory, and though I can hide my cold gaze and you can shake my hand and feel flesh gripping yours and maybe you can even sense our lifestyles are probably comparable: I simply am not there. It is hard for me to make sense on any given level. Myself is fabricated, an aberration. I am a noncontingent human being. My personality is sketchy and unformed, my heartlessness goes deep and is persistent. My conscience, my pity, my hopes disappeared a long time ago (probably at Harvard) if they ever did exist. There are no more barriers to cross.
Crime and Punishment is referenced in this chapter because a similarity between Raskolnikov's and Patrick's stories is being highlighted.
Both of them share a girl (Sonia and Jean) that cause the main character to change. Sonia makes Raskolnikov confess. Jean makes Patrick reexamine.
"What are you to do?" [Sonia] cried. "...Bow down to all the world and say to all men aloud, 'I am a murderer!'"
"I think it's ... time for me to ... take a good look ... at the world I've created," I choke, tearfully, finding myself admitting to her...
Some other comparisons is that they're both axe murderers and that their stories center around the anticipated consequences of murder. Besides those details, they are very much the opposite of each other.
Everything that Raskolnikov has, that Patrick doesn't, is the reason he gets the more better/happier(?) ending. (to be expanded laaaater)
Also bear with me in this upcoming sentence: "Like A Prayer" by Madonna is a song associated with Patrick and Jean's relationship.
The song mentioned thrice in the novel, each time happening when Patrick interacts with Jean.
“Jean?” I cry out. “Hello? Jean?” “Patrick? Is that you?” she calls back. “Hello?” “Jean, I need help,” I shout. [...] I hang up on her and lunge away from the phone booth and [...] a Madonna single, Madonna crying out, “life is a mystery, everyone must stand alone …,"
All summer long Madonna cries out to us, “life is a mystery, everyone must stand alone …”When I’m moving down Broadway to meet Jean, my secretary, for brunch...
A blast of music from a passing cab, Madonna again, “life is a mystery, everyone must stand alone …” Startled by the laughter atthe table next to ours, I cock my head and hear someone admit, “Sometimes what you wear to the office makes all the difference,” and then Jean says something and I ask her to repeat it.
For some context, in Crime and Punishment, Sonia is a devout Christian. She attempts to reinstill faith in Raskolnikov and gets him to repent for murder. Essentially, religion plays a big role in their relationship.
In the title alone, "Like A Prayer" is already a reference to religion. And I may be reaching, but... the lyrics also pertain to Patrick and Jean's relationship.
Like a child
You whisper softly to me
You're in control
Just like a child
For the first time I see Jean as uninhibited; she seems stronger, less controllable.[...]
I squeeze her hand back, moved, no, touched by her ignorance of evil.
Life is a mystery
Everyone must stand alone
“You’re sweet.” She rolls her eyes up. “Sweetness is … sexy … I don’t know. But so is … mystery.” Silence. “And I think … mystery … you’re mysterious.”
No end and no beginning
You're here with me
… where there was nature and earth, life and water, I saw a desert landscape that was unending.
The lyrics are also a metaphor of giving someone a blowjob. Which just fits within the context of the forever sex deprived life of Patrick Bateman.