What's the complement or corollary of "influences"?
If we were talking about people not books it would be follower or disciple. For a single thing, i.e. the book that takes after an earlier work, I think we need to use either:
- derivative -- most generally applicable choice
- sequel -- if it was very contingent or built upon the first
- offshoot -- if it continues or builds on the first but is not a pure continuation
And based on your edit I think what you are looking for is derivatives or offshoots.
Follows, derivative, imitative, aping, copying, wannabe, offshoot. And indeed, "influenced by".
If there are a great many, we may say that it was "in the tradition" of the earlier work, or even that it is part of a genre or movement that it (alone, or along with contemporaneous works) started. (Or perhaps founded if there was a conscious attempt to move in a particular artistic direction).
Follower, adherent, disciple, imitator, aper, copyist, wannabe & protégé can all apply to artists who came later, with different nuances as to the relationship to the earlier.
English speakers routinely add prefixes and suffixes to produce words from existing words. In this situation you can simply produce
influencee from influence
to get the meaning you want.
The -ee suffix means “the recipient of an action”. It comes from “the Anglo-French -é ending of [past participles] used as nouns.” It was originally used when writing law, and is still very commonly used in that context.¹ This is analogous to producing
educatee from educate
employee from employ
endorsee from endorse
enlistee from enlist
enrollee from enroll
evictee from evict
examinee from examine
illuminee from illumine
importee from import
indictee from indict
inductee from induct
interrogatee from interrogate
interviewee from interview
invitee from invite
and that is just considering a selection of verbs beginning with e and i.
The noun descendant is relevant, in its sense “(figuratively) A thing that derives directly from a given precursor or source [eg] This famous medieval manuscript has many descendants.” Also-used is children, from senses of child that include “(figuratively) An offspring” and “(figuratively) A thing or abstraction derived from or caused by something.” (For example, the 100+ companies that were offshoots of Fairchild Semiconductor, like AMD and Intel, have been called Fairchildren.)