Lexical Definition

‎συναγωνίζομαι‎ synagōnízomai (soon-ag-o-nid'-zom-ahee) to struggle ^G:V
from ‎σύν‎ and ‎ἀγωνίζομαι‎

strive together with.

• to struggle in company with, i.e. (figuratively) to be a partner (assistant)

Abbott-Smith

* συν-αγωνίζομαι
to strive together with, to help (prop., of sharing in a contest): c. dat. pers. et rei, Ro 15:30.†

Abbott-Smith References

Liddell-Scott-Jones

συναγωνίζομαι-ίζομαι,

Doric dialect aorist συναγωνιξάμην [Refs]:— contend along with, share in a contest, τινι with one, [NT+5th c.BC+]; μάχας [Refs 3rd c.BC+]

__b generally, ξ. τινί share in the fortunes of another, [Refs 5th c.BC+]
__2 aid, succour, τινι [Refs 4th c.BC+]; τινί τι one in a thing, [Refs]; τινὶ πρός τι one towards a thing, [Refs 4th c.BC+]: generally, assist, τῇ διατροπῇ [Refs 4th c.BC+]
__3 absolutely, fight on the same side, οἱ ξυναγωνιούμενοι [Refs 5th c.BC+]; of the Tragic chorus, join in the action, [Refs 4th c.BC+] —active -ίζω, uncertain reading in [Refs 1st c.BC+]

_{LSJ Scripture Refs: Rom.15.30}